diff --git a/specs/phase1/beacon-chain.md b/specs/phase1/beacon-chain.md
index fc9687545..611cc1955 100644
--- a/specs/phase1/beacon-chain.md
+++ b/specs/phase1/beacon-chain.md
@@ -33,7 +33,7 @@
   - [`AttestationCustodyBitWrapper`](#attestationcustodybitwrapper)
 - [Helper functions](#helper-functions)
   - [Misc](#misc-1)
-    - [`get_previous_slot`](#get_previous_slot)
+    - [`compute_previous_slot`](#compute_previous_slot)
     - [`pack_compact_validator`](#pack_compact_validator)
     - [`unpack_compact_validator`](#unpack_compact_validator)
     - [`committee_to_compact_committee`](#committee_to_compact_committee)
@@ -52,6 +52,7 @@
     - [`get_latest_slot_for_shard`](#get_latest_slot_for_shard)
     - [`get_offset_slots`](#get_offset_slots)
   - [Predicates](#predicates)
+    - [`is_shard_attestation`](#is_shard_attestation)
     - [`is_winning_attestation`](#is_winning_attestation)
     - [Updated `is_valid_indexed_attestation`](#updated-is_valid_indexed_attestation)
   - [Block processing](#block-processing)
@@ -369,10 +370,10 @@ class AttestationCustodyBitWrapper(Container):
 
 ### Misc
 
-#### `get_previous_slot`
+#### `compute_previous_slot`
 
 ```python
-def get_previous_slot(slot: Slot) -> Slot:
+def compute_previous_slot(slot: Slot) -> Slot:
     if slot > 0:
         return Slot(slot - 1)
     else:
@@ -556,6 +557,21 @@ def get_offset_slots(state: BeaconState, shard: Shard) -> Sequence[Slot]:
 
 ### Predicates
 
+#### `is_shard_attestation`
+
+```python
+def is_shard_attestation(state: BeaconState,
+                         attestation: Attestation,
+                         committee_index: CommitteeIndex) -> bool:
+    if not (
+        attestation.data.index == committee_index
+        and attestation.data.slot + MIN_ATTESTATION_INCLUSION_DELAY == state.slot
+    ):
+        return False
+
+    return True
+```
+
 #### `is_winning_attestation`
 
 ```python
@@ -568,7 +584,7 @@ def is_winning_attestation(state: BeaconState,
     ``winning_root`` formed by ``committee_index`` committee at the current slot.
     """
     return (
-        attestation.slot == state.slot
+        attestation.data.slot == state.slot
         and attestation.data.index == committee_index
         and attestation.data.shard_transition_root == winning_root
     )
@@ -623,9 +639,9 @@ def process_block(state: BeaconState, block: BeaconBlock) -> None:
     process_block_header(state, block)
     process_randao(state, block.body)
     process_eth1_data(state, block.body)
-    verify_shard_transition_false_positives(state, block.body)
     process_light_client_signatures(state, block.body)
     process_operations(state, block.body)
+    verify_shard_transition_false_positives(state, block.body)
 ```
 
 #### Operations
@@ -684,7 +700,7 @@ def validate_attestation(state: BeaconState, attestation: Attestation) -> None:
         # Correct data root count
         assert len(attestation.custody_bits_blocks) == len(get_offset_slots(state, shard))
         # Correct parent block root
-        assert data.beacon_block_root == get_block_root_at_slot(state, get_previous_slot(state.slot))
+        assert data.beacon_block_root == get_block_root_at_slot(state, compute_previous_slot(state.slot))
     # Type 2: no shard transition, no custody bits
     else:
         # Ensure delayed attestation
@@ -821,11 +837,12 @@ def process_crosslinks(state: BeaconState,
     for committee_index in map(CommitteeIndex, range(committee_count)):
         shard = compute_shard_from_committee_index(state, committee_index, state.slot)
         # All attestations in the block for this committee/shard and current slot
+        shard_transition = shard_transitions[shard]
         shard_attestations = [
             attestation for attestation in attestations
-            if attestation.data.index == committee_index and attestation.data.slot == state.slot
+            if is_shard_attestation(state, attestation, committee_index)
         ]
-        shard_transition = shard_transitions[shard]
+
         winning_root = process_crosslink_for_shard(state, committee_index, shard_transition, shard_attestations)
         if winning_root != Root():
             # Mark relevant pending attestations as creating a successful crosslink
@@ -920,10 +937,14 @@ def process_light_client_signatures(state: BeaconState, block_body: BeaconBlockB
 
     increase_balance(state, get_beacon_proposer_index(state), Gwei(total_reward // PROPOSER_REWARD_QUOTIENT))
 
-    slot = get_previous_slot(state.slot)
+    slot = compute_previous_slot(state.slot)
     signing_root = compute_signing_root(get_block_root_at_slot(state, slot),
                                         get_domain(state, DOMAIN_LIGHT_CLIENT, compute_epoch_at_slot(slot)))
-    assert bls.FastAggregateVerify(signer_pubkeys, signing_root, signature=block_body.light_client_signature)
+    if len(signer_pubkeys) == 0:
+        # TODO: Or disallow empty light_client_signature?
+        return
+    else:
+        assert bls.FastAggregateVerify(signer_pubkeys, signing_root, signature=block_body.light_client_signature)
 ```
 
 ### Epoch transition
diff --git a/specs/phase1/fraud-proofs.md b/specs/phase1/fraud-proofs.md
index a5068cd07..c676e142a 100644
--- a/specs/phase1/fraud-proofs.md
+++ b/specs/phase1/fraud-proofs.md
@@ -86,7 +86,6 @@ def verify_shard_block_message(beacon_state: BeaconState,
                                slot: Slot,
                                shard: Shard) -> bool:
     assert block.shard_parent_root == shard_state.latest_block_root
-    assert block.beacon_parent_root == get_block_root_at_slot(beacon_state, slot)
     assert block.slot == slot
     assert block.proposer_index == get_shard_proposer_index(beacon_state, slot, shard)
     assert 0 < len(block.body) <= MAX_SHARD_BLOCK_SIZE
@@ -124,7 +123,6 @@ def is_valid_fraud_proof(beacon_state: BeaconState,
                          subkey: BLSPubkey,
                          beacon_parent_block: BeaconBlock) -> bool:
     # 1. Check if `custody_bits[offset_index][j] != generate_custody_bit(subkey, block_contents)` for any `j`.
-    shard = get_shard(beacon_state, attestation)
     custody_bits = attestation.custody_bits_blocks
     for j in range(custody_bits[offset_index]):
         if custody_bits[offset_index][j] != generate_custody_bit(subkey, block):
@@ -133,6 +131,7 @@ def is_valid_fraud_proof(beacon_state: BeaconState,
     # 2. Check if the shard state transition result is wrong between
     # `transition.shard_states[offset_index - 1]` to `transition.shard_states[offset_index]`.
     if offset_index == 0:
+        shard = get_shard(beacon_state, attestation)
         shard_state = beacon_parent_block.shard_transitions[shard].shard_states[-1]
     else:
         shard_state = transition.shard_states[offset_index - 1]  # Not doing the actual state updates here.
diff --git a/specs/phase1/phase1-fork.md b/specs/phase1/phase1-fork.md
index e95c12c72..cc7d8f33e 100644
--- a/specs/phase1/phase1-fork.md
+++ b/specs/phase1/phase1-fork.md
@@ -103,7 +103,7 @@ def upgrade_to_phase1(pre: phase0.BeaconState) -> BeaconState:
             ShardState(
                 slot=pre.slot,
                 gasprice=MIN_GASPRICE,
-                data=Root(),
+                transition_digest=Root(),
                 latest_block_root=Root(),
             ) for i in range(INITIAL_ACTIVE_SHARDS)
         ),
@@ -111,7 +111,7 @@ def upgrade_to_phase1(pre: phase0.BeaconState) -> BeaconState:
         current_light_committee=CompactCommittee(),  # computed after state creation
         next_light_committee=CompactCommittee(),
         # Custody game
-        custody_challenge_index=0,
+        exposed_derived_secrets=[] * EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS,
         # exposed_derived_secrets will fully default to zeroes
     )
     next_epoch = Epoch(epoch + 1)
diff --git a/tests/core/pyspec/eth2spec/test/helpers/attestations.py b/tests/core/pyspec/eth2spec/test/helpers/attestations.py
index c203b737a..9e98e83ea 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/attestations.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/attestations.py
@@ -1,7 +1,7 @@
 from typing import List
 
 from eth2spec.test.context import expect_assertion_error, PHASE0, PHASE1
-from eth2spec.test.helpers.state import state_transition_and_sign_block
+from eth2spec.test.helpers.state import state_transition_and_sign_block, next_slot, transition_to
 from eth2spec.test.helpers.block import build_empty_block_for_next_slot
 from eth2spec.test.helpers.keys import privkeys
 from eth2spec.utils import bls
@@ -43,7 +43,7 @@ def run_attestation_processing(spec, state, attestation, valid=True):
     yield 'post', state
 
 
-def build_attestation_data(spec, state, slot, index, shard_transition=None):
+def build_attestation_data(spec, state, slot, index, shard_transition=None, on_time=True):
     assert state.slot >= slot
 
     if slot == state.slot:
@@ -66,28 +66,42 @@ def build_attestation_data(spec, state, slot, index, shard_transition=None):
         source_epoch = state.current_justified_checkpoint.epoch
         source_root = state.current_justified_checkpoint.root
 
-    if spec.fork == PHASE1 and shard_transition is not None:
-        shard_transition_root = shard_transition.hash_tree_root()
-        head_shard_root = shard_transition.shard_data_roots[len(shard_transition.shard_data_roots) - 1]
-    else:
-        shard_transition_root = spec.Root()
-        head_shard_root = spec.Root()
-
-    return spec.AttestationData(
+    attestation_data = spec.AttestationData(
         slot=slot,
         index=index,
         beacon_block_root=block_root,
         source=spec.Checkpoint(epoch=source_epoch, root=source_root),
         target=spec.Checkpoint(epoch=spec.compute_epoch_at_slot(slot), root=epoch_boundary_root),
-        head_shard_root=head_shard_root,
-        shard_transition_root=shard_transition_root,
     )
 
+    if spec.fork == PHASE1:
+        if shard_transition is not None:
+            lastest_shard_data_root_index = len(shard_transition.shard_data_roots) - 1
+            attestation_data.head_shard_root = shard_transition.shard_data_roots[lastest_shard_data_root_index]
+            attestation_data.shard_transition_root = shard_transition.hash_tree_root()
+        else:
+            # No shard transition
+            shard = spec.get_shard(state, spec.Attestation(data=attestation_data))
+            if on_time:
+                temp_state = state.copy()
+                next_slot(spec, temp_state)
+                shard_transition = spec.get_shard_transition(temp_state, shard, [])
+                lastest_shard_data_root_index = len(shard_transition.shard_data_roots) - 1
+                attestation_data.head_shard_root = shard_transition.shard_data_roots[lastest_shard_data_root_index]
+                attestation_data.shard_transition_root = shard_transition.hash_tree_root()
+            else:
+                attestation_data.head_shard_root = state.shard_states[shard].transition_digest
+                attestation_data.shard_transition_root = spec.Root()
+    return attestation_data
+
 
 def convert_to_valid_on_time_attestation(spec, state, attestation, signed=False):
     shard = spec.get_shard(state, attestation)
-    offset_slots = spec.compute_offset_slots(spec.get_latest_slot_for_shard(state, shard), state.slot + 1)
-    for offset_slot in offset_slots:
+    offset_slots = spec.compute_offset_slots(
+        spec.get_latest_slot_for_shard(state, shard),
+        attestation.data.slot + spec.MIN_ATTESTATION_INCLUSION_DELAY,
+    )
+    for _ in offset_slots:
         attestation.custody_bits_blocks.append(
             Bitlist[spec.MAX_VALIDATORS_PER_COMMITTEE]([0 for _ in attestation.aggregation_bits])
         )
@@ -143,7 +157,9 @@ def get_valid_attestation(spec,
     if index is None:
         index = 0
 
-    attestation_data = build_attestation_data(spec, state, slot=slot, index=index, shard_transition=shard_transition)
+    attestation_data = build_attestation_data(
+        spec, state, slot=slot, index=index, shard_transition=shard_transition, on_time=on_time
+    )
 
     beacon_committee = spec.get_beacon_committee(
         state,
@@ -298,7 +314,21 @@ def next_epoch_with_attestations(spec,
                     spec, post_state, slot_to_attest, index=index, signed=True, on_time=False)
                 block.body.attestations.append(prev_attestation)
 
+        if spec.fork == PHASE1:
+            fill_block_shard_transitions_by_attestations(spec, post_state, block)
+
         signed_block = state_transition_and_sign_block(spec, post_state, block)
         signed_blocks.append(signed_block)
 
     return state, signed_blocks, post_state
+
+
+def fill_block_shard_transitions_by_attestations(spec, state, block):
+    block.body.shard_transitions = [spec.ShardTransition()] * spec.MAX_SHARDS
+    for attestation in block.body.attestations:
+        shard = spec.get_shard(state, attestation)
+        if attestation.data.slot == state.slot:
+            temp_state = state.copy()
+            transition_to(spec, temp_state, slot=block.slot)
+            shard_transition = spec.get_shard_transition(temp_state, shard, [])
+            block.body.shard_transitions[shard] = shard_transition
diff --git a/tests/core/pyspec/eth2spec/test/helpers/block.py b/tests/core/pyspec/eth2spec/test/helpers/block.py
index 96cc30e35..e40d5e7d8 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/block.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/block.py
@@ -71,24 +71,31 @@ def build_empty_block(spec, state, slot=None):
     """
     if slot is None:
         slot = state.slot
-    if slot < state.slot:
-        raise Exception("build_empty_block cannot build blocks for past slots")
-    if slot > state.slot:
-        # transition forward in copied state to grab relevant data from state
-        state = state.copy()
-        spec.process_slots(state, slot)
 
+    state, parent_block_root = get_state_and_beacon_parent_root_at_slot(spec, state, slot)
     empty_block = spec.BeaconBlock()
     empty_block.slot = slot
     empty_block.proposer_index = spec.get_beacon_proposer_index(state)
     empty_block.body.eth1_data.deposit_count = state.eth1_deposit_index
-    previous_block_header = state.latest_block_header.copy()
-    if previous_block_header.state_root == spec.Root():
-        previous_block_header.state_root = hash_tree_root(state)
-    empty_block.parent_root = hash_tree_root(previous_block_header)
+    empty_block.parent_root = parent_block_root
     apply_randao_reveal(spec, state, empty_block)
     return empty_block
 
 
 def build_empty_block_for_next_slot(spec, state):
     return build_empty_block(spec, state, state.slot + 1)
+
+
+def get_state_and_beacon_parent_root_at_slot(spec, state, slot):
+    if slot < state.slot:
+        raise Exception("Cannot build blocks for past slots")
+    if slot > state.slot:
+        # transition forward in copied state to grab relevant data from state
+        state = state.copy()
+        spec.process_slots(state, slot)
+
+    previous_block_header = state.latest_block_header.copy()
+    if previous_block_header.state_root == spec.Root():
+        previous_block_header.state_root = hash_tree_root(state)
+    beacon_parent_root = hash_tree_root(previous_block_header)
+    return state, beacon_parent_root
diff --git a/tests/core/pyspec/eth2spec/test/helpers/shard_block.py b/tests/core/pyspec/eth2spec/test/helpers/shard_block.py
index 25d868b65..922f4d748 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/shard_block.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/shard_block.py
@@ -1,3 +1,6 @@
+from eth2spec.test.helpers.attestations import get_valid_on_time_attestation
+from eth2spec.test.helpers.block import get_state_and_beacon_parent_root_at_slot
+from eth2spec.test.helpers.state import next_slots
 from eth2spec.test.helpers.keys import privkeys
 from eth2spec.utils import bls
 from eth2spec.utils.bls import only_with_bls
@@ -18,21 +21,22 @@ def sign_shard_block(spec, beacon_state, shard, block, proposer_index=None):
 def build_shard_block(spec,
                       beacon_state,
                       shard,
-                      slot,
+                      slot=None,
                       body=None,
                       signed=False):
     shard_state = beacon_state.shard_states[shard]
     if slot is None:
-        slot = shard_state.slot
+        slot = shard_state.slot + 1
 
     if body is None:
-        body = []
+        body = b'\x56' * 128
 
     proposer_index = spec.get_shard_proposer_index(beacon_state, slot, shard)
+    beacon_state, beacon_parent_root = get_state_and_beacon_parent_root_at_slot(spec, beacon_state, slot)
 
     block = spec.ShardBlock(
         shard_parent_root=shard_state.latest_block_root,
-        beacon_parent_root=spec.get_block_root_at_slot(beacon_state, spec.get_previous_slot(slot)),
+        beacon_parent_root=beacon_parent_root,
         slot=slot,
         proposer_index=proposer_index,
         body=body,
@@ -45,3 +49,40 @@ def build_shard_block(spec,
         sign_shard_block(spec, beacon_state, shard, signed_block, proposer_index=proposer_index)
 
     return signed_block
+
+
+def build_shard_transitions_till_slot(spec, state, shards, shard_blocks, target_len_offset_slot):
+    state = state.copy()
+    next_slots(spec, state, target_len_offset_slot)
+    shard_transitions = [spec.ShardTransition()] * spec.MAX_SHARDS
+    for shard in shards:
+        offset_slots = spec.get_offset_slots(state, shard)
+        len_offset_slots = len(offset_slots)
+        assert len_offset_slots == target_len_offset_slot
+        shard_blocks_of_shard = shard_blocks[shard]
+        shard_transition = spec.get_shard_transition(state, shard, shard_blocks_of_shard)
+        if len(shard_blocks_of_shard) > 0:
+            shard_block_root = shard_blocks_of_shard[-1].message.hash_tree_root()
+            assert shard_transition.shard_states[len_offset_slots - 1].latest_block_root == shard_block_root
+            assert shard_transition.shard_states[len_offset_slots - 1].slot == offset_slots[-1]
+        shard_transitions[shard] = shard_transition
+
+    return shard_transitions
+
+
+def build_attestation_with_shard_transition(spec, state, slot, index, target_len_offset_slot, shard_transition=None):
+    state = state.copy()
+    next_slots(spec, state, target_len_offset_slot)
+    attestation = get_valid_on_time_attestation(
+        spec,
+        state,
+        slot=slot,
+        index=index,
+        shard_transition=shard_transition,
+        signed=True,
+    )
+    assert attestation.data.slot == slot
+    if shard_transition is not None:
+        assert target_len_offset_slot == len(shard_transition.shard_states)
+        assert attestation.data.shard_transition_root == shard_transition.hash_tree_root()
+    return attestation
diff --git a/tests/core/pyspec/eth2spec/test/phase_0/sanity/test_blocks.py b/tests/core/pyspec/eth2spec/test/phase_0/sanity/test_blocks.py
index b6b671872..29a9dcca2 100644
--- a/tests/core/pyspec/eth2spec/test/phase_0/sanity/test_blocks.py
+++ b/tests/core/pyspec/eth2spec/test/phase_0/sanity/test_blocks.py
@@ -8,10 +8,13 @@ from eth2spec.test.helpers.block import build_empty_block_for_next_slot, build_e
 from eth2spec.test.helpers.keys import privkeys, pubkeys
 from eth2spec.test.helpers.attester_slashings import get_valid_attester_slashing, get_indexed_attestation_participants
 from eth2spec.test.helpers.proposer_slashings import get_valid_proposer_slashing
-from eth2spec.test.helpers.attestations import get_valid_attestation
+from eth2spec.test.helpers.attestations import get_valid_attestation, fill_block_shard_transitions_by_attestations
 from eth2spec.test.helpers.deposits import prepare_state_and_deposit
 
-from eth2spec.test.context import spec_state_test, with_all_phases, expect_assertion_error, always_bls, with_phases
+from eth2spec.test.context import (
+    spec_state_test, with_all_phases, expect_assertion_error, always_bls, with_phases,
+    PHASE1
+)
 
 
 @with_all_phases
@@ -420,12 +423,14 @@ def test_attestation(spec, state):
 
     yield 'pre', state
 
-    attestation = get_valid_attestation(spec, state, signed=True)
+    attestation = get_valid_attestation(spec, state, signed=True, on_time=True)
 
     # Add to state via block transition
     pre_current_attestations_len = len(state.current_epoch_attestations)
     attestation_block = build_empty_block(spec, state, state.slot + spec.MIN_ATTESTATION_INCLUSION_DELAY)
     attestation_block.body.attestations.append(attestation)
+    if spec.fork == PHASE1:
+        fill_block_shard_transitions_by_attestations(spec, state, attestation_block)
     signed_attestation_block = state_transition_and_sign_block(spec, state, attestation_block)
 
     assert len(state.current_epoch_attestations) == pre_current_attestations_len + 1
diff --git a/tests/core/pyspec/eth2spec/test/phase_1/block_processing/test_process_crosslink.py b/tests/core/pyspec/eth2spec/test/phase_1/block_processing/test_process_crosslink.py
index 6d1e65678..912770da8 100644
--- a/tests/core/pyspec/eth2spec/test/phase_1/block_processing/test_process_crosslink.py
+++ b/tests/core/pyspec/eth2spec/test/phase_1/block_processing/test_process_crosslink.py
@@ -1,101 +1,78 @@
 from eth2spec.test.context import (
+    PHASE0,
     with_all_phases_except,
     spec_state_test,
     always_bls,
 )
-from eth2spec.test.helpers.attestations import (
-    get_valid_on_time_attestation,
+from eth2spec.test.helpers.crosslinks import run_crosslinks_processing
+from eth2spec.test.helpers.shard_block import (
+    build_attestation_with_shard_transition,
+    build_shard_block,
+    build_shard_transitions_till_slot,
 )
-from eth2spec.test.helpers.crosslinks import (
-    run_crosslinks_processing,
-)
-from eth2spec.test.helpers.shard_block import build_shard_block
-from eth2spec.test.helpers.state import next_epoch, next_slot, next_slots
+from eth2spec.test.helpers.state import next_epoch, next_slot, transition_to
 
 
-@with_all_phases_except(['phase0'])
+def run_basic_crosslink_tests(spec, state, target_len_offset_slot):
+    next_epoch(spec, state)
+    next_epoch(spec, state)
+    state = spec.upgrade_to_phase1(state)
+    next_slot(spec, state)
+
+    # At the beginning, let `x = state.slot`, `state.shard_states[shard].slot == x - 1`
+    slot_x = state.slot
+    committee_index = spec.CommitteeIndex(0)
+    shard = spec.compute_shard_from_committee_index(state, committee_index, state.slot)
+    assert state.shard_states[shard].slot == slot_x - 1
+
+    # Create SignedShardBlock at slot `shard_state.slot + 1` -> x
+    body = b'\x56' * spec.MAX_SHARD_BLOCK_SIZE
+    shard_block = build_shard_block(spec, state, shard, body=body, signed=True)
+    shard_blocks = [shard_block]
+
+    # Attester creates `attestation` at slot x
+    # Use temporary next state to get ShardTransition of shard block
+    shard_transitions = build_shard_transitions_till_slot(
+        spec,
+        state,
+        shards=[shard, ],
+        shard_blocks={shard: shard_blocks},
+        target_len_offset_slot=target_len_offset_slot,
+    )
+    shard_transition = shard_transitions[shard]
+    attestation = build_attestation_with_shard_transition(
+        spec,
+        state,
+        slot=slot_x + target_len_offset_slot - 1,
+        index=committee_index,
+        target_len_offset_slot=target_len_offset_slot,
+        shard_transition=shard_transition,
+    )
+    pre_gasprice = state.shard_states[shard].gasprice
+
+    transition_to(spec, state, state.slot + spec.MIN_ATTESTATION_INCLUSION_DELAY)
+    pre_shard_state = state.shard_states[shard]
+    yield from run_crosslinks_processing(spec, state, shard_transitions, [attestation])
+
+    # After state transition,
+    assert state.slot == slot_x + target_len_offset_slot
+    shard_state = state.shard_states[shard]
+    assert shard_state != pre_shard_state
+    assert shard_state == shard_transition.shard_states[len(shard_transition.shard_states) - 1]
+
+    if target_len_offset_slot == 1:
+        assert shard_state.gasprice > pre_gasprice
+
+
+@with_all_phases_except([PHASE0])
 @spec_state_test
 @always_bls
 def test_basic_crosslinks(spec, state):
-    next_epoch(spec, state)
-    next_epoch(spec, state)
-    state = spec.upgrade_to_phase1(state)
-    next_slot(spec, state)
-
-    committee_index = spec.CommitteeIndex(0)
-    shard = spec.compute_shard_from_committee_index(state, committee_index, state.slot)
-    body = b'1' * spec.MAX_SHARD_BLOCK_SIZE
-    shard_block = build_shard_block(spec, state, shard, body=body, slot=state.slot, signed=True)
-    shard_blocks = [shard_block]
-
-    next_slot(spec, state)
-
-    shard_transition = spec.get_shard_transition(state, shard, shard_blocks)
-    shard_transitions = [spec.ShardTransition()] * len(state.shard_states)
-    shard_transitions[shard] = shard_transition
-
-    attestation = get_valid_on_time_attestation(
-        spec,
-        state,
-        slot=state.slot,
-        index=committee_index,
-        shard_transition=shard_transition,
-        signed=True,
-    )
-    attestations = [attestation]
-
-    pre_gasprice = state.shard_states[shard].gasprice
-    offset_slots = spec.get_offset_slots(state, shard)
-    assert len(offset_slots) == 1
-
-    yield from run_crosslinks_processing(spec, state, shard_transitions, attestations)
-
-    shard_state = state.shard_states[shard]
-    assert shard_state.slot == offset_slots[-1]
-    assert shard_state.latest_block_root == shard_block.message.hash_tree_root()
-    assert shard_state == shard_transition.shard_states[len(shard_transition.shard_states) - 1]
-    assert shard_state.gasprice > pre_gasprice
+    run_basic_crosslink_tests(spec, state, target_len_offset_slot=1)
 
 
-@with_all_phases_except(['phase0'])
+@with_all_phases_except([PHASE0])
 @spec_state_test
 @always_bls
 def test_multiple_offset_slots(spec, state):
-    next_epoch(spec, state)
-    next_epoch(spec, state)
-    state = spec.upgrade_to_phase1(state)
-    next_slot(spec, state)
-
-    committee_index = spec.CommitteeIndex(0)
-    shard = spec.compute_shard_from_committee_index(state, committee_index, state.slot)
-    body = b'1' * spec.MAX_SHARD_BLOCK_SIZE
-    shard_block = build_shard_block(spec, state, shard, body=body, slot=state.slot, signed=True)
-    shard_blocks = [shard_block]
-
-    next_slots(spec, state, 3)
-
-    shard_transition = spec.get_shard_transition(state, shard, shard_blocks)
-    shard_transitions = [spec.ShardTransition()] * len(state.shard_states)
-    shard_transitions[shard] = shard_transition
-
-    attestation = get_valid_on_time_attestation(
-        spec,
-        state,
-        slot=state.slot,
-        index=committee_index,
-        shard_transition=shard_transition,
-        signed=True,
-    )
-    attestations = [attestation]
-
-    pre_gasprice = state.shard_states[shard].gasprice
-    offset_slots = spec.get_offset_slots(state, shard)
-    assert len(offset_slots) == 3
-
-    yield from run_crosslinks_processing(spec, state, shard_transitions, attestations)
-
-    shard_state = state.shard_states[shard]
-    assert shard_state.slot == offset_slots[-1]
-    assert shard_state.latest_block_root == shard_block.message.hash_tree_root()
-    assert shard_state == shard_transition.shard_states[len(shard_transition.shard_states) - 1]
-    assert shard_state.gasprice > pre_gasprice
+    run_basic_crosslink_tests(spec, state, target_len_offset_slot=3)
diff --git a/tests/core/pyspec/eth2spec/test/phase_1/sanity/__init__.py b/tests/core/pyspec/eth2spec/test/phase_1/sanity/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/core/pyspec/eth2spec/test/phase_1/sanity/test_blocks.py b/tests/core/pyspec/eth2spec/test/phase_1/sanity/test_blocks.py
new file mode 100644
index 000000000..168915d02
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/phase_1/sanity/test_blocks.py
@@ -0,0 +1,141 @@
+from eth2spec.test.context import (
+    PHASE0,
+    with_all_phases_except,
+    spec_state_test,
+    always_bls,
+)
+from eth2spec.test.helpers.block import build_empty_block
+from eth2spec.test.helpers.shard_block import (
+    build_attestation_with_shard_transition,
+    build_shard_block,
+    build_shard_transitions_till_slot,
+)
+from eth2spec.test.helpers.state import next_epoch, next_slot, state_transition_and_sign_block
+
+
+@with_all_phases_except([PHASE0])
+@spec_state_test
+@always_bls
+def test_process_beacon_block_with_normal_shard_transition(spec, state):
+    next_epoch(spec, state)
+    next_epoch(spec, state)
+    state = spec.upgrade_to_phase1(state)
+    next_slot(spec, state)
+
+    target_len_offset_slot = 1
+
+    # At the beginning, let `x = state.slot`, `state.shard_states[shard].slot == x - 1`
+    slot_x = state.slot
+    committee_index = spec.CommitteeIndex(0)
+    shard = spec.compute_shard_from_committee_index(state, committee_index, state.slot)
+    assert state.shard_states[shard].slot == slot_x - 1
+
+    # Create SignedShardBlock at slot `shard_state.slot + 1` -> x
+    body = b'\x56' * spec.MAX_SHARD_BLOCK_SIZE
+    shard_block = build_shard_block(spec, state, shard, body=body, signed=True)
+    shard_blocks = [shard_block]
+
+    # Attester creates `attestation` at slot x
+    # Use temporary next state to get ShardTransition of shard block
+    shard_transitions = build_shard_transitions_till_slot(
+        spec,
+        state,
+        shards=[shard, ],
+        shard_blocks={shard: shard_blocks},
+        target_len_offset_slot=target_len_offset_slot,
+    )
+    shard_transition = shard_transitions[shard]
+    attestation = build_attestation_with_shard_transition(
+        spec,
+        state,
+        slot=slot_x + target_len_offset_slot - 1,
+        index=committee_index,
+        target_len_offset_slot=target_len_offset_slot,
+        shard_transition=shard_transition,
+    )
+    pre_gasprice = state.shard_states[shard].gasprice
+
+    # Propose beacon block at slot `x + 1`
+    pre_shard_state = state.shard_states[shard]
+    beacon_block_1 = build_empty_block(spec, state, slot=slot_x + target_len_offset_slot)
+    beacon_block_1.body.attestations = [attestation]
+    beacon_block_1.body.shard_transitions = shard_transitions
+    assert (
+        beacon_block_1.slot == slot_x + target_len_offset_slot
+        == shard_transition.shard_states[0].slot + target_len_offset_slot
+    )
+    state_transition_and_sign_block(spec, state, beacon_block_1)
+
+    # After state transition
+    assert state.slot == slot_x + target_len_offset_slot
+    shard_state = state.shard_states[shard]
+    # latest_block_root has changed
+    assert shard_state.latest_block_root == shard_block.message.hash_tree_root()
+    assert shard_state != pre_shard_state
+    assert shard_state == shard_transition.shard_states[len(shard_transition.shard_states) - 1]
+
+    if target_len_offset_slot == 1 and len(shard_blocks) > 0:
+        assert shard_state.gasprice > pre_gasprice
+
+
+@with_all_phases_except([PHASE0])
+@spec_state_test
+@always_bls
+def test_process_beacon_block_with_empty_proposal_transition(spec, state):
+    next_epoch(spec, state)
+    next_epoch(spec, state)
+    state = spec.upgrade_to_phase1(state)
+    next_slot(spec, state)
+
+    target_len_offset_slot = 1
+
+    # At the beginning, let `x = state.slot`, `state.shard_states[shard].slot == x - 1`
+    slot_x = state.slot
+    committee_index = spec.CommitteeIndex(0)
+    shard = spec.compute_shard_from_committee_index(state, committee_index, state.slot)
+    assert state.shard_states[shard].slot == slot_x - 1
+
+    # No new shard block
+    shard_blocks = []
+
+    # Attester creates `attestation` at slot x
+    # Use temporary next state to get ShardTransition of shard block
+    shard_transitions = build_shard_transitions_till_slot(
+        spec,
+        state,
+        shards=[shard, ],
+        shard_blocks={shard: shard_blocks},
+        target_len_offset_slot=target_len_offset_slot,
+    )
+    shard_transition = shard_transitions[shard]
+    attestation = build_attestation_with_shard_transition(
+        spec,
+        state,
+        slot=slot_x + target_len_offset_slot - 1,
+        index=committee_index,
+        target_len_offset_slot=target_len_offset_slot,
+        shard_transition=shard_transition,
+    )
+    pre_gasprice = state.shard_states[shard].gasprice
+
+    # Propose beacon block at slot `x + 1`
+    pre_shard_state = state.shard_states[shard]
+    beacon_block_1 = build_empty_block(spec, state, slot=slot_x + target_len_offset_slot)
+    beacon_block_1.body.attestations = [attestation]
+    beacon_block_1.body.shard_transitions = shard_transitions
+    assert (
+        beacon_block_1.slot == slot_x + target_len_offset_slot
+        == shard_transition.shard_states[0].slot + target_len_offset_slot
+    )
+    state_transition_and_sign_block(spec, state, beacon_block_1)
+
+    # After state transition
+    assert state.slot == slot_x + target_len_offset_slot
+    shard_state = state.shard_states[shard]
+    # latest_block_root hasn't changed
+    assert shard_state.latest_block_root == pre_shard_state.latest_block_root
+    assert shard_state != pre_shard_state
+    assert shard_state == shard_transition.shard_states[len(shard_transition.shard_states) - 1]
+
+    if target_len_offset_slot == 1 and len(shard_blocks) > 0:
+        assert shard_state.gasprice > pre_gasprice