diff --git a/changelog.d/8032.misc b/changelog.d/8032.misc
new file mode 100644
index 000000000..dfe4c0317
--- /dev/null
+++ b/changelog.d/8032.misc
@@ -0,0 +1 @@
+Convert various parts of the codebase to async/await.
diff --git a/synapse/handlers/appservice.py b/synapse/handlers/appservice.py
index fbc56c351..c9044a501 100644
--- a/synapse/handlers/appservice.py
+++ b/synapse/handlers/appservice.py
@@ -101,7 +101,7 @@ class ApplicationServicesHandler(object):
 
                             async def start_scheduler():
                                 try:
-                                    return self.scheduler.start()
+                                    return await self.scheduler.start()
                                 except Exception:
                                     logger.error("Application Services Failure")
 
diff --git a/synapse/http/site.py b/synapse/http/site.py
index 6f3b2258c..f506152fe 100644
--- a/synapse/http/site.py
+++ b/synapse/http/site.py
@@ -146,10 +146,9 @@ class SynapseRequest(Request):
 
         Returns a context manager; the correct way to use this is:
 
-        @defer.inlineCallbacks
-        def handle_request(request):
+        async def handle_request(request):
             with request.processing("FooServlet"):
-                yield really_handle_the_request()
+                await really_handle_the_request()
 
         Once the context manager is closed, the completion of the request will be logged,
         and the various metrics will be updated.
diff --git a/synapse/metrics/background_process_metrics.py b/synapse/metrics/background_process_metrics.py
index a9269196b..f766d16db 100644
--- a/synapse/metrics/background_process_metrics.py
+++ b/synapse/metrics/background_process_metrics.py
@@ -13,16 +13,15 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import inspect
 import logging
 import threading
-from asyncio import iscoroutine
 from functools import wraps
 from typing import TYPE_CHECKING, Dict, Optional, Set
 
 from prometheus_client.core import REGISTRY, Counter, Gauge
 
 from twisted.internet import defer
-from twisted.python.failure import Failure
 
 from synapse.logging.context import LoggingContext, PreserveLoggingContext
 
@@ -167,7 +166,7 @@ class _BackgroundProcess(object):
         )
 
 
-def run_as_background_process(desc, func, *args, **kwargs):
+def run_as_background_process(desc: str, func, *args, **kwargs):
     """Run the given function in its own logcontext, with resource metrics
 
     This should be used to wrap processes which are fired off to run in the
@@ -179,7 +178,7 @@ def run_as_background_process(desc, func, *args, **kwargs):
     normal synapse inlineCallbacks function).
 
     Args:
-        desc (str): a description for this background process type
+        desc: a description for this background process type
         func: a function, which may return a Deferred or a coroutine
         args: positional args for func
         kwargs: keyword args for func
@@ -188,8 +187,7 @@ def run_as_background_process(desc, func, *args, **kwargs):
         follow the synapse logcontext rules.
     """
 
-    @defer.inlineCallbacks
-    def run():
+    async def run():
         with _bg_metrics_lock:
             count = _background_process_counts.get(desc, 0)
             _background_process_counts[desc] = count + 1
@@ -203,29 +201,21 @@ def run_as_background_process(desc, func, *args, **kwargs):
             try:
                 result = func(*args, **kwargs)
 
-                # We probably don't have an ensureDeferred in our call stack to handle
-                # coroutine results, so we need to ensureDeferred here.
-                #
-                # But we need this check because ensureDeferred doesn't like being
-                # called on immediate values (as opposed to Deferreds or coroutines).
-                if iscoroutine(result):
-                    result = defer.ensureDeferred(result)
+                if inspect.isawaitable(result):
+                    result = await result
 
-                return (yield result)
+                return result
             except Exception:
-                # failure.Failure() fishes the original Failure out of our stack, and
-                # thus gives us a sensible stack trace.
-                f = Failure()
-                logger.error(
-                    "Background process '%s' threw an exception",
-                    desc,
-                    exc_info=(f.type, f.value, f.getTracebackObject()),
+                logger.exception(
+                    "Background process '%s' threw an exception", desc,
                 )
             finally:
                 _background_process_in_flight_count.labels(desc).dec()
 
     with PreserveLoggingContext():
-        return run()
+        # Note that we return a Deferred here so that it can be used in a
+        # looping_call and other places that expect a Deferred.
+        return defer.ensureDeferred(run())
 
 
 def wrap_as_background_process(desc):