diff --git a/sentry_sdk/integrations/wsgi.py b/sentry_sdk/integrations/wsgi.py
index f91f10ac67..9a098b6697 100644
--- a/sentry_sdk/integrations/wsgi.py
+++ b/sentry_sdk/integrations/wsgi.py
@@ -87,7 +87,7 @@ def __call__(self, environ, start_response):
 
             try:
                 rv = self.app(environ, start_response)
-            except Exception:
+            except BaseException:
                 reraise(*_capture_exception(hub))
 
         return _ScopedResponse(hub, rv)
@@ -151,15 +151,22 @@ def get_client_ip(environ):
 
 def _capture_exception(hub):
     # type: (Hub) -> ExcInfo
+    exc_info = sys.exc_info()
+
     # Check client here as it might have been unset while streaming response
     if hub.client is not None:
-        exc_info = sys.exc_info()
-        event, hint = event_from_exception(
-            exc_info,
-            client_options=hub.client.options,
-            mechanism={"type": "wsgi", "handled": False},
-        )
-        hub.capture_event(event, hint=hint)
+        e = exc_info[1]
+
+        # SystemExit(0) is the only uncaught exception that is expected behavior
+        should_skip_capture = isinstance(e, SystemExit) and e.code in (0, None)
+        if not should_skip_capture:
+            event, hint = event_from_exception(
+                exc_info,
+                client_options=hub.client.options,
+                mechanism={"type": "wsgi", "handled": False},
+            )
+            hub.capture_event(event, hint=hint)
+
     return exc_info
 
 
@@ -181,7 +188,7 @@ def __iter__(self):
                     chunk = next(iterator)
                 except StopIteration:
                     break
-                except Exception:
+                except BaseException:
                     reraise(*_capture_exception(self._hub))
 
             yield chunk
@@ -192,7 +199,7 @@ def close(self):
                 self._response.close()
             except AttributeError:
                 pass
-            except Exception:
+            except BaseException:
                 reraise(*_capture_exception(self._hub))
 
 
diff --git a/tests/integrations/wsgi/test_wsgi.py b/tests/integrations/wsgi/test_wsgi.py
index b63540c3f6..be26496e98 100644
--- a/tests/integrations/wsgi/test_wsgi.py
+++ b/tests/integrations/wsgi/test_wsgi.py
@@ -12,6 +12,28 @@ def app(environ, start_response):
     return app
 
 
+class IterableApp(object):
+    def __init__(self, iterable):
+        self.iterable = iterable
+
+    def __call__(self, environ, start_response):
+        return self.iterable
+
+
+class ExitingIterable(object):
+    def __init__(self, exc_func):
+        self._exc_func = exc_func
+
+    def __iter__(self):
+        return self
+
+    def __next__(self):
+        raise self._exc_func()
+
+    def next(self):
+        return type(self).__next__(self)
+
+
 def test_basic(sentry_init, crashing_app, capture_events):
     sentry_init(send_default_pii=True)
     app = SentryWsgiMiddleware(crashing_app)
@@ -30,3 +52,58 @@ def test_basic(sentry_init, crashing_app, capture_events):
         "query_string": "",
         "url": "http://localhost/",
     }
+
+
+@pytest.fixture(params=[0, None])
+def test_systemexit_zero_is_ignored(sentry_init, capture_events, request):
+    zero_code = request.param
+    sentry_init(send_default_pii=True)
+    iterable = ExitingIterable(lambda: SystemExit(zero_code))
+    app = SentryWsgiMiddleware(IterableApp(iterable))
+    client = Client(app)
+    events = capture_events()
+
+    with pytest.raises(SystemExit):
+        client.get("/")
+
+    assert len(events) == 0
+
+
+@pytest.fixture(params=["", "foo", 1, 2])
+def test_systemexit_nonzero_is_captured(sentry_init, capture_events, request):
+    nonzero_code = request.param
+    sentry_init(send_default_pii=True)
+    iterable = ExitingIterable(lambda: SystemExit(nonzero_code))
+    app = SentryWsgiMiddleware(IterableApp(iterable))
+    client = Client(app)
+    events = capture_events()
+
+    with pytest.raises(SystemExit):
+        client.get("/")
+
+    event, = events
+
+    assert "exception" in event
+    exc = event["exception"]["values"][-1]
+    assert exc["type"] == "SystemExit"
+    assert exc["value"] == nonzero_code
+    assert event["level"] == "error"
+
+
+def test_keyboard_interrupt_is_captured(sentry_init, capture_events):
+    sentry_init(send_default_pii=True)
+    iterable = ExitingIterable(lambda: KeyboardInterrupt())
+    app = SentryWsgiMiddleware(IterableApp(iterable))
+    client = Client(app)
+    events = capture_events()
+
+    with pytest.raises(KeyboardInterrupt):
+        client.get("/")
+
+    event, = events
+
+    assert "exception" in event
+    exc = event["exception"]["values"][-1]
+    assert exc["type"] == "KeyboardInterrupt"
+    assert exc["value"] == ""
+    assert event["level"] == "error"