diff --git a/specs/core/0_fork-choice.md b/specs/core/0_fork-choice.md
index 051c6ef8d..13d451c3e 100644
--- a/specs/core/0_fork-choice.md
+++ b/specs/core/0_fork-choice.md
@@ -238,6 +238,12 @@ def on_block(store: Store, block: BeaconBlock) -> None:
 
 ```python
 def on_attestation(store: Store, attestation: Attestation) -> None:
+    """
+    Run ``on_attestation`` upon receiving a new ``attestation`` from either within a block or directly on the wire.
+
+    An ``attestation`` that is asserted as invalid may be valid at a later time,
+    consider scheduling it for later processing in such case.
+    """
     target = attestation.data.target
 
     # Attestations must be from the current or previous epoch 
@@ -248,10 +254,17 @@ def on_attestation(store: Store, attestation: Attestation) -> None:
     # Cannot calculate the current shuffling if have not seen the target
     assert target.root in store.blocks
 
+    # Attestations target be for a known block. If target block is unknown, delay consideration until the block is found
+    assert target.root in store.blocks
     # Attestations cannot be from future epochs. If they are, delay consideration until the epoch arrives
     base_state = store.block_states[target.root].copy()
     assert store.time >= base_state.genesis_time + compute_start_slot_at_epoch(target.epoch) * SECONDS_PER_SLOT
 
+    # Attestations must be for a known block. If block is unknown, delay consideration until the block is found
+    assert attestation.data.beacon_block_root in store.blocks
+    # Attestations must not be for blocks in the future. If not, the attestation should not be considered
+    assert store.blocks[attestation.data.beacon_block_root].slot <= attestation.data.slot
+
     # Store target checkpoint state if not yet seen
     if target not in store.checkpoint_states:
         process_slots(base_state, compute_start_slot_at_epoch(target.epoch))
diff --git a/test_libs/pyspec/eth2spec/test/fork_choice/test_on_attestation.py b/test_libs/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
index 8db55cce8..50e3fc070 100644
--- a/test_libs/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
+++ b/test_libs/pyspec/eth2spec/test/fork_choice/test_on_attestation.py
@@ -1,8 +1,7 @@
-
 from eth2spec.test.context import with_all_phases, spec_state_test
 from eth2spec.test.helpers.block import build_empty_block_for_next_slot
-from eth2spec.test.helpers.attestations import get_valid_attestation
-from eth2spec.test.helpers.state import state_transition_and_sign_block
+from eth2spec.test.helpers.attestations import get_valid_attestation, sign_attestation
+from eth2spec.test.helpers.state import transition_to, state_transition_and_sign_block
 
 
 def run_on_attestation(spec, state, store, attestation, valid=True):
@@ -89,18 +88,48 @@ def test_on_attestation_past_epoch(spec, state):
 @spec_state_test
 def test_on_attestation_target_not_in_store(spec, state):
     store = spec.get_genesis_store(state)
-    time = 100
+    time = spec.SECONDS_PER_SLOT * spec.SLOTS_PER_EPOCH
     spec.on_tick(store, time)
 
-    # move to next epoch to make block new target
-    state.slot += spec.SLOTS_PER_EPOCH
+    # move to immediately before next epoch to make block new target
+    transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH - 1)
 
-    block = build_empty_block_for_next_slot(spec, state)
-    state_transition_and_sign_block(spec, state, block)
+    target_block = build_empty_block_for_next_slot(spec, state)
+    state_transition_and_sign_block(spec, state, target_block)
 
-    # do not add block to store
+    # do not add target block to store
+
+    attestation = get_valid_attestation(spec, state, slot=target_block.slot)
+    assert attestation.data.target.root == target_block.signing_root()
+
+    run_on_attestation(spec, state, store, attestation, False)
+
+
+@with_all_phases
+@spec_state_test
+def test_on_attestation_beacon_block_not_in_store(spec, state):
+    store = spec.get_genesis_store(state)
+    time = spec.SECONDS_PER_SLOT * spec.SLOTS_PER_EPOCH
+    spec.on_tick(store, time)
+
+    # move to immediately before next epoch to make block new target
+    transition_to(spec, state, state.slot + spec.SLOTS_PER_EPOCH - 1)
+
+    target_block = build_empty_block_for_next_slot(spec, state)
+    state_transition_and_sign_block(spec, state, target_block)
+
+    # store target in store
+    spec.on_block(store, target_block)
+
+    head_block = build_empty_block_for_next_slot(spec, state)
+    state_transition_and_sign_block(spec, state, head_block)
+
+    # do not add head block to store
+
+    attestation = get_valid_attestation(spec, state, slot=head_block.slot)
+    assert attestation.data.target.root == target_block.signing_root()
+    assert attestation.data.beacon_block_root == head_block.signing_root()
 
-    attestation = get_valid_attestation(spec, state, slot=block.slot)
     run_on_attestation(spec, state, store, attestation, False)
 
 
@@ -124,6 +153,26 @@ def test_on_attestation_future_epoch(spec, state):
     run_on_attestation(spec, state, store, attestation, False)
 
 
+@with_all_phases
+@spec_state_test
+def test_on_attestation_future_block(spec, state):
+    store = spec.get_genesis_store(state)
+    time = spec.SECONDS_PER_SLOT * 5
+    spec.on_tick(store, time)
+
+    block = build_empty_block_for_next_slot(spec, state)
+    state_transition_and_sign_block(spec, state, block)
+
+    spec.on_block(store, block)
+
+    # attestation for slot immediately prior to the block being attested to
+    attestation = get_valid_attestation(spec, state, slot=block.slot - 1, signed=False)
+    attestation.data.beacon_block_root = block.signing_root()
+    sign_attestation(spec, state, attestation)
+
+    run_on_attestation(spec, state, store, attestation, False)
+
+
 @with_all_phases
 @spec_state_test
 def test_on_attestation_same_slot(spec, state):
diff --git a/test_libs/pyspec/eth2spec/test/helpers/state.py b/test_libs/pyspec/eth2spec/test/helpers/state.py
index 27e946cbb..a26621c84 100644
--- a/test_libs/pyspec/eth2spec/test/helpers/state.py
+++ b/test_libs/pyspec/eth2spec/test/helpers/state.py
@@ -14,6 +14,16 @@ def next_slot(spec, state):
     spec.process_slots(state, state.slot + 1)
 
 
+def transition_to(spec, state, slot):
+    """
+    Transition to ``slot``.
+    """
+    assert state.slot <= slot
+    for _ in range(slot - state.slot):
+        next_slot(spec, state)
+    assert state.slot == slot
+
+
 def next_epoch(spec, state):
     """
     Transition to the start slot of the next epoch