diff --git a/doc/source/tune-usage.rst b/doc/source/tune-usage.rst
index c9e18fcf7..2a6bcf2eb 100644
--- a/doc/source/tune-usage.rst
+++ b/doc/source/tune-usage.rst
@@ -106,7 +106,7 @@ All results reported by the trainable will be logged locally to a unique directo
 Trial Parallelism
 ~~~~~~~~~~~~~~~~~
 
-Tune automatically N concurrent trials, where N is the number of CPUs (cores) on your machine. By default, Tune assumes that each trial will only require 1 CPU. You can override this with ``resources_per_trial``:
+Tune automatically runs N concurrent trials, where N is the number of CPUs (cores) on your machine. By default, Tune assumes that each trial will only require 1 CPU. You can override this with ``resources_per_trial``:
 
 .. code-block:: python
 
@@ -474,6 +474,41 @@ You often will want to compute a large object (e.g., training data, model weight
 
     tune.run(f)
 
+Custom Stopping Criteria
+------------------------
+
+You can control when trials are stopped early by passing the ``stop`` argument to ``tune.run``. This argument takes either a dictionary or a function.
+
+If a dictionary is passed in, the keys may be any field in the return result of ``tune.track.log`` in the Function API or ``train()`` (including the results from ``_train`` and auto-filled metrics).
+
+In the example below, each trial will be stopped either when it completes 10 iterations OR when it reaches a mean accuracy of 0.98. Note that `training_iteration` is an auto-filled metric by Tune.
+
+.. code-block:: python
+
+    tune.run(
+        my_trainable,
+        stop={"training_iteration": 10, "mean_accuracy": 0.98}
+    )
+
+For more flexibility, you can pass in a function instead. If a function is passed in, it must take ``(trial_id, result)`` as arguments and return a boolean (``True`` if trial should be stopped and ``False`` otherwise).
+
+You can use this to stop all trials after the criteria is fulfilled by any individual trial:
+
+.. code-block:: python
+
+    class Stopper:
+        def __init__(self):
+            self.should_stop = False
+
+        def stop(self, trial_id, result):
+            if not self.should_stop and result['foo'] > 10:
+                self.should_stop = True
+            return self.should_stop
+
+    stopper = Stopper()
+    tune.run(my_trainable, stop=stopper.stop)
+
+Note that in the above example all trials will not stop immediately, but will do so once their current iterations are complete.
 
 Auto-Filled Results
 -------------------
diff --git a/python/ray/tune/experiment.py b/python/ray/tune/experiment.py
index 1af9b043f..baa958191 100644
--- a/python/ray/tune/experiment.py
+++ b/python/ray/tune/experiment.py
@@ -3,6 +3,7 @@ from __future__ import division
 from __future__ import print_function
 
 import copy
+import inspect
 import logging
 import os
 import six
@@ -87,11 +88,19 @@ class Experiment(object):
             _raise_deprecation_note(
                 "sync_function", "sync_to_driver", soft=False)
 
+        stop = stop or {}
+        if not isinstance(stop, dict) and not callable(stop):
+            raise ValueError("Invalid stop criteria: {}. Must be a callable "
+                             "or dict".format(stop))
+        if callable(stop) and len(inspect.getargspec(stop).args) != 2:
+            raise ValueError("Invalid stop criteria: {}. Callable criteria "
+                             "must take exactly 2 parameters.".format(stop))
+
         config = config or {}
         run_identifier = Experiment._register_if_needed(run)
         spec = {
             "run": run_identifier,
-            "stop": stop or {},
+            "stop": stop,
             "config": config,
             "resources_per_trial": resources_per_trial,
             "num_samples": num_samples,
diff --git a/python/ray/tune/tests/test_trial_runner.py b/python/ray/tune/tests/test_trial_runner.py
index f37fa327a..f1785f0dd 100644
--- a/python/ray/tune/tests/test_trial_runner.py
+++ b/python/ray/tune/tests/test_trial_runner.py
@@ -453,6 +453,17 @@ class TrainableFunctionApiTest(unittest.TestCase):
         [trial] = tune.run(train, stop={"test/test1/test2": 6}).trials
         self.assertEqual(trial.last_result["training_iteration"], 7)
 
+    def testStoppingFunction(self):
+        def train(config, reporter):
+            for i in range(10):
+                reporter(test=i)
+
+        def stop(trial_id, result):
+            return result["test"] > 6
+
+        [trial] = tune.run(train, stop=stop).trials
+        self.assertEqual(trial.last_result["training_iteration"], 8)
+
     def testEarlyReturn(self):
         def train(config, reporter):
             reporter(timesteps_total=100, done=True)
diff --git a/python/ray/tune/trial.py b/python/ray/tune/trial.py
index b0de00bd3..725ce04fb 100644
--- a/python/ray/tune/trial.py
+++ b/python/ray/tune/trial.py
@@ -284,6 +284,9 @@ class Trial(object):
         if result.get(DONE):
             return True
 
+        if callable(self.stopping_criterion):
+            return self.stopping_criterion(self.trial_id, result)
+
         for criteria, stop_value in self.stopping_criterion.items():
             if criteria not in result:
                 raise TuneError(
diff --git a/python/ray/tune/tune.py b/python/ray/tune/tune.py
index 881751823..73747c449 100644
--- a/python/ray/tune/tune.py
+++ b/python/ray/tune/tune.py
@@ -80,9 +80,11 @@ def run(run_or_experiment,
             If Experiment, then Tune will execute training based on
             Experiment.spec.
         name (str): Name of experiment.
-        stop (dict): The stopping criteria. The keys may be any field in
-            the return result of 'train()', whichever is reached first.
-            Defaults to empty dict.
+        stop (dict|func): The stopping criteria. If dict, the keys may be
+            any field in the return result of 'train()', whichever is
+            reached first. If function, it must take (trial_id, result) as
+            arguments and return a boolean (True if trial should be stopped,
+            False otherwise).
         config (dict): Algorithm-specific configuration for Tune variant
             generation (e.g. env, hyperparams). Defaults to empty dict.
             Custom search algorithms may ignore this.