diff --git a/discord/ext/tasks/__init__.py b/discord/ext/tasks/__init__.py
index 89070594a..bba436d45 100644
--- a/discord/ext/tasks/__init__.py
+++ b/discord/ext/tasks/__init__.py
@@ -5,6 +5,8 @@ import websockets
 import discord
 import inspect
 import logging
+import sys
+import traceback
 
 from discord.backoff import ExponentialBackoff
 
@@ -50,15 +52,15 @@ class Loop:
         if not inspect.iscoroutinefunction(self.coro):
             raise TypeError('Expected coroutine function, not {0.__name__!r}.'.format(type(self.coro)))
 
-    async def _call_loop_function(self, name):
+    async def _call_loop_function(self, name, *args, **kwargs):
         coro = getattr(self, '_' + name)
         if coro is None:
             return
 
         if self._injected is not None:
-            await coro(self._injected)
+            await coro(self._injected, *args, **kwargs)
         else:
-            await coro()
+            await coro(*args, **kwargs)
 
     async def _loop(self, *args, **kwargs):
         backoff = ExponentialBackoff()
@@ -89,10 +91,10 @@ class Loop:
         except asyncio.CancelledError:
             self._is_being_cancelled = True
             raise
-        except Exception:
+        except Exception as exc:
             self._has_failed = True
-            log.exception('Internal background task failed.')
-            raise
+            await self._call_loop_function('error', exc)
+            raise exc
         finally:
             await self._call_loop_function('after_loop')
             self._is_being_cancelled = False
@@ -283,6 +285,10 @@ class Loop:
         """
         return not bool(self._task.done()) if self._task else False
 
+    async def _error(self, exception):
+        print('Unhandled exception in internal background task {0.__name__!r}.'.format(self.coro), file=sys.stderr)
+        traceback.print_exception(type(exception), exception, exception.__traceback__, file=sys.stderr)
+
     def before_loop(self, coro):
         """A decorator that registers a coroutine to be called before the loop starts running.
 
@@ -336,6 +342,32 @@ class Loop:
         self._after_loop = coro
         return coro
 
+    def error(self, coro):
+        """A decorator that registers a coroutine to be called if the task encounters an unhandled exception.
+
+        The coroutine must take only one argument the exception raised (except ``self`` in a class context).
+
+        By default this prints to :data:`sys.stderr` however it could be
+        overridden to have a different implementation.
+
+        .. versionadded:: 1.4
+
+        Parameters
+        ------------
+        coro: :ref:`coroutine <coroutine>`
+            The coroutine to register in the event of an unhandled exception.
+
+        Raises
+        -------
+        TypeError
+            The function was not a coroutine.
+        """
+        if not inspect.iscoroutinefunction(coro):
+            raise TypeError('Expected coroutine function, received {0.__name__!r}.'.format(type(coro)))
+
+        self._error = coro
+        return coro
+
     def _get_next_sleep_time(self):
         return self._last_iteration + datetime.timedelta(seconds=self._sleep)