diff --git a/changelog.d/8507.misc b/changelog.d/8507.misc
new file mode 100644
index 0000000000..724da8a996
--- /dev/null
+++ b/changelog.d/8507.misc
@@ -0,0 +1 @@
+ Add type hints to various parts of the code base.
diff --git a/mypy.ini b/mypy.ini
index 19b60f7534..f08fe992a4 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -65,6 +65,7 @@ files =
   synapse/types.py,
   synapse/util/async_helpers.py,
   synapse/util/caches/descriptors.py,
+  synapse/util/caches/response_cache.py,
   synapse/util/caches/stream_change_cache.py,
   synapse/util/metrics.py,
   tests/replication,
diff --git a/synapse/appservice/api.py b/synapse/appservice/api.py
index c526c28b93..e8f0793795 100644
--- a/synapse/appservice/api.py
+++ b/synapse/appservice/api.py
@@ -14,7 +14,7 @@
 # limitations under the License.
 import logging
 import urllib
-from typing import TYPE_CHECKING, Optional
+from typing import TYPE_CHECKING, Optional, Tuple
 
 from prometheus_client import Counter
 
@@ -93,7 +93,7 @@ class ApplicationServiceApi(SimpleHttpClient):
 
         self.protocol_meta_cache = ResponseCache(
             hs, "as_protocol_meta", timeout_ms=HOUR_IN_MS
-        )
+        )  # type: ResponseCache[Tuple[str, str]]
 
     async def query_user(self, service, user_id):
         if service.url is None:
diff --git a/synapse/federation/federation_server.py b/synapse/federation/federation_server.py
index e8039e244c..23278e36b7 100644
--- a/synapse/federation/federation_server.py
+++ b/synapse/federation/federation_server.py
@@ -116,7 +116,7 @@ class FederationServer(FederationBase):
         # We cache results for transaction with the same ID
         self._transaction_resp_cache = ResponseCache(
             hs, "fed_txn_handler", timeout_ms=30000
-        )
+        )  # type: ResponseCache[Tuple[str, str]]
 
         self.transaction_actions = TransactionActions(self.store)
 
@@ -124,10 +124,12 @@ class FederationServer(FederationBase):
 
         # We cache responses to state queries, as they take a while and often
         # come in waves.
-        self._state_resp_cache = ResponseCache(hs, "state_resp", timeout_ms=30000)
+        self._state_resp_cache = ResponseCache(
+            hs, "state_resp", timeout_ms=30000
+        )  # type: ResponseCache[Tuple[str, str]]
         self._state_ids_resp_cache = ResponseCache(
             hs, "state_ids_resp", timeout_ms=30000
-        )
+        )  # type: ResponseCache[Tuple[str, str]]
 
         self._federation_metrics_domains = (
             hs.get_config().federation.federation_metrics_domains
diff --git a/synapse/handlers/initial_sync.py b/synapse/handlers/initial_sync.py
index 39a85801c1..98075f48d2 100644
--- a/synapse/handlers/initial_sync.py
+++ b/synapse/handlers/initial_sync.py
@@ -14,7 +14,7 @@
 # limitations under the License.
 
 import logging
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, Optional, Tuple
 
 from twisted.internet import defer
 
@@ -47,12 +47,14 @@ class InitialSyncHandler(BaseHandler):
         self.state = hs.get_state_handler()
         self.clock = hs.get_clock()
         self.validator = EventValidator()
-        self.snapshot_cache = ResponseCache(hs, "initial_sync_cache")
+        self.snapshot_cache = ResponseCache(
+            hs, "initial_sync_cache"
+        )  # type: ResponseCache[Tuple[str, Optional[StreamToken], Optional[StreamToken], str, Optional[int], bool, bool]]
         self._event_serializer = hs.get_event_client_serializer()
         self.storage = hs.get_storage()
         self.state_store = self.storage.state
 
-    def snapshot_all_rooms(
+    async def snapshot_all_rooms(
         self,
         user_id: str,
         pagin_config: PaginationConfig,
@@ -84,7 +86,7 @@ class InitialSyncHandler(BaseHandler):
             include_archived,
         )
 
-        return self.snapshot_cache.wrap(
+        return await self.snapshot_cache.wrap(
             key,
             self._snapshot_all_rooms,
             user_id,
diff --git a/synapse/handlers/room.py b/synapse/handlers/room.py
index 1d04d41e98..93ed51063a 100644
--- a/synapse/handlers/room.py
+++ b/synapse/handlers/room.py
@@ -120,7 +120,7 @@ class RoomCreationHandler(BaseHandler):
         # subsequent requests
         self._upgrade_response_cache = ResponseCache(
             hs, "room_upgrade", timeout_ms=FIVE_MINUTES_IN_MS
-        )
+        )  # type: ResponseCache[Tuple[str, str]]
         self._server_notices_mxid = hs.config.server_notices_mxid
 
         self.third_party_event_rules = hs.get_third_party_event_rules()
diff --git a/synapse/handlers/sync.py b/synapse/handlers/sync.py
index 6fb8332f93..a306631094 100644
--- a/synapse/handlers/sync.py
+++ b/synapse/handlers/sync.py
@@ -243,7 +243,9 @@ class SyncHandler:
         self.presence_handler = hs.get_presence_handler()
         self.event_sources = hs.get_event_sources()
         self.clock = hs.get_clock()
-        self.response_cache = ResponseCache(hs, "sync")
+        self.response_cache = ResponseCache(
+            hs, "sync"
+        )  # type: ResponseCache[Tuple[Any, ...]]
         self.state = hs.get_state_handler()
         self.auth = hs.get_auth()
         self.storage = hs.get_storage()
diff --git a/synapse/replication/http/_base.py b/synapse/replication/http/_base.py
index 64edadb624..2b3972cb14 100644
--- a/synapse/replication/http/_base.py
+++ b/synapse/replication/http/_base.py
@@ -92,7 +92,7 @@ class ReplicationEndpoint(metaclass=abc.ABCMeta):
         if self.CACHE:
             self.response_cache = ResponseCache(
                 hs, "repl." + self.NAME, timeout_ms=30 * 60 * 1000
-            )
+            )  # type: ResponseCache[str]
 
         # We reserve `instance_name` as a parameter to sending requests, so we
         # assert here that sub classes don't try and use the name.
diff --git a/synapse/util/caches/response_cache.py b/synapse/util/caches/response_cache.py
index df1a721add..32228f42ee 100644
--- a/synapse/util/caches/response_cache.py
+++ b/synapse/util/caches/response_cache.py
@@ -13,6 +13,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 import logging
+from typing import TYPE_CHECKING, Any, Callable, Dict, Generic, Optional, TypeVar
 
 from twisted.internet import defer
 
@@ -20,10 +21,15 @@ from synapse.logging.context import make_deferred_yieldable, run_in_background
 from synapse.util.async_helpers import ObservableDeferred
 from synapse.util.caches import register_cache
 
+if TYPE_CHECKING:
+    from synapse.app.homeserver import HomeServer
+
 logger = logging.getLogger(__name__)
 
+T = TypeVar("T")
 
-class ResponseCache:
+
+class ResponseCache(Generic[T]):
     """
     This caches a deferred response. Until the deferred completes it will be
     returned from the cache. This means that if the client retries the request
@@ -31,8 +37,9 @@ class ResponseCache:
     used rather than trying to compute a new response.
     """
 
-    def __init__(self, hs, name, timeout_ms=0):
-        self.pending_result_cache = {}  # Requests that haven't finished yet.
+    def __init__(self, hs: "HomeServer", name: str, timeout_ms: float = 0):
+        # Requests that haven't finished yet.
+        self.pending_result_cache = {}  # type: Dict[T, ObservableDeferred]
 
         self.clock = hs.get_clock()
         self.timeout_sec = timeout_ms / 1000.0
@@ -40,13 +47,13 @@ class ResponseCache:
         self._name = name
         self._metrics = register_cache("response_cache", name, self, resizable=False)
 
-    def size(self):
+    def size(self) -> int:
         return len(self.pending_result_cache)
 
-    def __len__(self):
+    def __len__(self) -> int:
         return self.size()
 
-    def get(self, key):
+    def get(self, key: T) -> Optional[defer.Deferred]:
         """Look up the given key.
 
         Can return either a new Deferred (which also doesn't follow the synapse
@@ -58,12 +65,11 @@ class ResponseCache:
         from an absent cache entry.
 
         Args:
-            key (hashable):
+            key: key to get/set in the cache
 
         Returns:
-            twisted.internet.defer.Deferred|None|E: None if there is no entry
-            for this key; otherwise either a deferred result or the result
-            itself.
+            None if there is no entry for this key; otherwise a deferred which
+            resolves to the result.
         """
         result = self.pending_result_cache.get(key)
         if result is not None:
@@ -73,7 +79,7 @@ class ResponseCache:
             self._metrics.inc_misses()
             return None
 
-    def set(self, key, deferred):
+    def set(self, key: T, deferred: defer.Deferred) -> defer.Deferred:
         """Set the entry for the given key to the given deferred.
 
         *deferred* should run its callbacks in the sentinel logcontext (ie,
@@ -85,12 +91,11 @@ class ResponseCache:
         result. You will probably want to make_deferred_yieldable the result.
 
         Args:
-            key (hashable):
-            deferred (twisted.internet.defer.Deferred[T):
+            key: key to get/set in the cache
+            deferred: The deferred which resolves to the result.
 
         Returns:
-            twisted.internet.defer.Deferred[T]|T: a new deferred, or the actual
-                result.
+            A new deferred which resolves to the actual result.
         """
         result = ObservableDeferred(deferred, consumeErrors=True)
         self.pending_result_cache[key] = result
@@ -107,7 +112,9 @@ class ResponseCache:
         result.addBoth(remove)
         return result.observe()
 
-    def wrap(self, key, callback, *args, **kwargs):
+    def wrap(
+        self, key: T, callback: "Callable[..., Any]", *args: Any, **kwargs: Any
+    ) -> defer.Deferred:
         """Wrap together a *get* and *set* call, taking care of logcontexts
 
         First looks up the key in the cache, and if it is present makes it
@@ -118,21 +125,20 @@ class ResponseCache:
 
         Example usage:
 
-            @defer.inlineCallbacks
-            def handle_request(request):
+            async def handle_request(request):
                 # etc
                 return result
 
-            result = yield response_cache.wrap(
+            result = await response_cache.wrap(
                 key,
                 handle_request,
                 request,
             )
 
         Args:
-            key (hashable): key to get/set in the cache
+            key: key to get/set in the cache
 
-            callback (callable): function to call if the key is not found in
+            callback: function to call if the key is not found in
                 the cache
 
             *args: positional parameters to pass to the callback, if it is used
@@ -140,7 +146,7 @@ class ResponseCache:
             **kwargs: named parameters to pass to the callback, if it is used
 
         Returns:
-            twisted.internet.defer.Deferred: yieldable result
+            Deferred which resolves to the result
         """
         result = self.get(key)
         if not result: