diff --git a/CHANGELOG.md b/CHANGELOG.md
index b2e4107ef5ff8a..cdb9ddc804d72c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -17,6 +17,8 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Added multiclass AUROC metric ([#4236](https://github.com/PyTorchLightning/pytorch-lightning/pull/4236))
 
+- Added global step indexing to the checkpoint name for a better sub-epoch checkpointing experience ([#3807](https://github.com/PyTorchLightning/pytorch-lightning/pull/3807)) 
+
 ### Changed
 
 - W&B log in sync with Trainer step ([#4405](https://github.com/PyTorchLightning/pytorch-lightning/pull/4405))
diff --git a/pytorch_lightning/callbacks/model_checkpoint.py b/pytorch_lightning/callbacks/model_checkpoint.py
index 33ed1d71d9eb4d..f3eabf5611cf00 100644
--- a/pytorch_lightning/callbacks/model_checkpoint.py
+++ b/pytorch_lightning/callbacks/model_checkpoint.py
@@ -101,7 +101,7 @@ class ModelCheckpoint(Callback):
                 ...     filename='{epoch}-{val_loss:.2f}-{other_metric:.2f}'
                 ... )
 
-            By default, filename is ``None`` and will be set to ``'{epoch}'``.
+            By default, filename is ``None`` and will be set to ``'{epoch}-{step}'``.
 
 
     Example::
@@ -222,16 +222,16 @@ def save_checkpoint(self, trainer, pl_module):
         monitor_candidates = self._monitor_candidates(trainer)
 
         # ie: path/val_loss=0.5.ckpt
-        filepath = self._get_metric_interpolated_filepath_name(epoch, monitor_candidates)
+        filepath = self._get_metric_interpolated_filepath_name(monitor_candidates, epoch, global_step)
 
         # callback supports multiple simultaneous modes
         # here we call each mode sequentially
         # Mode 1: save all checkpoints OR only the top k
         if self.save_top_k:
-            self._save_top_k_checkpoints(monitor_candidates, trainer, pl_module, epoch, filepath)
+            self._save_top_k_checkpoints(monitor_candidates, trainer, pl_module, filepath)
 
         # Mode 2: save the last checkpoint
-        self._save_last_checkpoint(trainer, pl_module, epoch, monitor_candidates, filepath)
+        self._save_last_checkpoint(trainer, pl_module, monitor_candidates, filepath)
 
     def __validate_init_configuration(self):
         if self.save_top_k is not None and self.save_top_k < -1:
@@ -360,16 +360,17 @@ def _format_checkpoint_name(
         cls,
         filename: Optional[str],
         epoch: int,
+        step: int,
         metrics: Dict[str, Any],
         prefix: str = "",
     ) -> str:
         if not filename:
             # filename is not set, use default name
-            filename = "{epoch}"
+            filename = "{epoch}-{step}"
         # check and parse user passed keys in the string
         groups = re.findall(r"(\{.*?)[:\}]", filename)
         if len(groups) >= 0:
-            metrics["epoch"] = epoch
+            metrics.update({"epoch": epoch, 'step': step})
             for group in groups:
                 name = group[1:]
                 filename = filename.replace(group, name + "={" + name)
@@ -379,7 +380,7 @@ def _format_checkpoint_name(
         return cls.CHECKPOINT_JOIN_CHAR.join([txt for txt in (prefix, filename) if txt])
 
     def format_checkpoint_name(
-        self, epoch: int, metrics: Dict[str, Any], ver: Optional[int] = None
+        self, epoch: int, step: int, metrics: Dict[str, Any], ver: Optional[int] = None
     ) -> str:
         """Generate a filename according to the defined template.
 
@@ -387,24 +388,24 @@ def format_checkpoint_name(
 
             >>> tmpdir = os.path.dirname(__file__)
             >>> ckpt = ModelCheckpoint(dirpath=tmpdir, filename='{epoch}')
-            >>> os.path.basename(ckpt.format_checkpoint_name(0, {}))
+            >>> os.path.basename(ckpt.format_checkpoint_name(0, 1, metrics={}))
             'epoch=0.ckpt'
             >>> ckpt = ModelCheckpoint(dirpath=tmpdir, filename='{epoch:03d}')
-            >>> os.path.basename(ckpt.format_checkpoint_name(5, {}))
+            >>> os.path.basename(ckpt.format_checkpoint_name(5, 2, metrics={}))
             'epoch=005.ckpt'
             >>> ckpt = ModelCheckpoint(dirpath=tmpdir, filename='{epoch}-{val_loss:.2f}')
-            >>> os.path.basename(ckpt.format_checkpoint_name(2, dict(val_loss=0.123456)))
+            >>> os.path.basename(ckpt.format_checkpoint_name(2, 3, metrics=dict(val_loss=0.123456)))
             'epoch=2-val_loss=0.12.ckpt'
             >>> ckpt = ModelCheckpoint(dirpath=tmpdir, filename='{missing:d}')
-            >>> os.path.basename(ckpt.format_checkpoint_name(0, {}))
+            >>> os.path.basename(ckpt.format_checkpoint_name(0, 4, metrics={}))
             'missing=0.ckpt'
-            >>> ckpt = ModelCheckpoint(filename='{epoch}')
-            >>> os.path.basename(ckpt.format_checkpoint_name(0, {}))
-            'epoch=0.ckpt'
+            >>> ckpt = ModelCheckpoint(filename='{step}')
+            >>> os.path.basename(ckpt.format_checkpoint_name(0, 0, {}))
+            'step=0.ckpt'
 
         """
         filename = self._format_checkpoint_name(
-            self.filename, epoch, metrics, prefix=self.prefix
+            self.filename, epoch, step, metrics, prefix=self.prefix
         )
         if ver is not None:
             filename = self.CHECKPOINT_JOIN_CHAR.join((filename, f"v{ver}"))
@@ -479,13 +480,11 @@ def _validate_monitor_key(self, trainer):
             )
             raise MisconfigurationException(m)
 
-    def _get_metric_interpolated_filepath_name(self, epoch, ckpt_name_metrics):
-        filepath = self.format_checkpoint_name(epoch, ckpt_name_metrics)
+    def _get_metric_interpolated_filepath_name(self, ckpt_name_metrics: Dict[str, Any], epoch: int, step: int):
+        filepath = self.format_checkpoint_name(epoch, step, ckpt_name_metrics)
         version_cnt = 0
         while self._fs.exists(filepath):
-            filepath = self.format_checkpoint_name(
-                epoch, ckpt_name_metrics, ver=version_cnt
-            )
+            filepath = self.format_checkpoint_name(epoch, step, ckpt_name_metrics, ver=version_cnt)
             # this epoch called before
             version_cnt += 1
         return filepath
@@ -494,9 +493,10 @@ def _monitor_candidates(self, trainer):
         ckpt_name_metrics = deepcopy(trainer.logger_connector.logged_metrics)
         ckpt_name_metrics.update(trainer.logger_connector.callback_metrics)
         ckpt_name_metrics.update(trainer.logger_connector.progress_bar_metrics)
+        ckpt_name_metrics.update({"step": trainer.global_step, "epoch": trainer.current_epoch})
         return ckpt_name_metrics
 
-    def _save_last_checkpoint(self, trainer, pl_module, epoch, ckpt_name_metrics, filepath):
+    def _save_last_checkpoint(self, trainer, pl_module, ckpt_name_metrics, filepath):
         should_save_last = self.monitor is None or self.save_last
         if not should_save_last:
             return
@@ -506,7 +506,11 @@ def _save_last_checkpoint(self, trainer, pl_module, epoch, ckpt_name_metrics, fi
         # when user ALSO asked for the 'last.ckpt' change the name
         if self.save_last:
             last_filepath = self._format_checkpoint_name(
-                self.CHECKPOINT_NAME_LAST, epoch, ckpt_name_metrics, prefix=self.prefix
+                self.CHECKPOINT_NAME_LAST,
+                trainer.current_epoch,
+                trainer.global_step,
+                ckpt_name_metrics,
+                prefix=self.prefix
             )
             last_filepath = os.path.join(self.dirpath, f"{last_filepath}.ckpt")
 
@@ -523,17 +527,19 @@ def _save_last_checkpoint(self, trainer, pl_module, epoch, ckpt_name_metrics, fi
         if self.monitor is None:
             self.best_model_path = self.last_model_path
 
-    def _save_top_k_checkpoints(self, metrics, trainer, pl_module, epoch, filepath):
+    def _save_top_k_checkpoints(self, metrics, trainer, pl_module, filepath):
         current = metrics.get(self.monitor)
+        epoch = metrics.get("epoch")
+        step = metrics.get("step")
 
         if not isinstance(current, torch.Tensor) and current is not None:
             current = torch.tensor(current, device=pl_module.device)
 
         if self.check_monitor_top_k(current):
-            self._update_best_and_save(filepath, current, epoch, trainer, pl_module)
+            self._update_best_and_save(filepath, current, epoch, step, trainer, pl_module)
         elif self.verbose:
             rank_zero_info(
-                f"Epoch {epoch:d}: {self.monitor} was not in top {self.save_top_k}"
+                f"Epoch {epoch:d}, step {step:d}: {self.monitor} was not in top {self.save_top_k}"
             )
 
     def _is_valid_monitor_key(self, metrics):
@@ -544,11 +550,11 @@ def _update_best_and_save(
         filepath: str,
         current: torch.Tensor,
         epoch: int,
+        step: int,
         trainer,
         pl_module,
     ):
-
-        k = epoch + 1 if self.save_top_k == -1 else self.save_top_k
+        k = len(self.best_k_models) + 1 if self.save_top_k == -1 else self.save_top_k
 
         del_list = []
         if len(self.best_k_models) == k and k > 0:
@@ -575,9 +581,8 @@ def _update_best_and_save(
 
         if self.verbose:
             rank_zero_info(
-                f"Epoch {epoch:d}: {self.monitor} reached"
-                f" {current:0.5f} (best {self.best_model_score:0.5f}),"
-                f" saving model to {filepath} as top {k}"
+                f"Epoch {epoch:d}, global step {step:d}: {self.monitor} reached {current:0.5f}"
+                f' (best {self.best_model_score:0.5f}), saving model to "{filepath}" as top {k}'
             )
         self._save_model(filepath, trainer, pl_module)
 
diff --git a/pytorch_lightning/trainer/evaluation_loop.py b/pytorch_lightning/trainer/evaluation_loop.py
index 9dab036583dd85..ffc72f8f0022e8 100644
--- a/pytorch_lightning/trainer/evaluation_loop.py
+++ b/pytorch_lightning/trainer/evaluation_loop.py
@@ -250,9 +250,10 @@ def __run_eval_epoch_end(self, num_dataloaders, using_eval_result):
         # depre warning
         if eval_results is not None and user_reduced:
             step = 'testing_epoch_end' if self.testing else 'validation_epoch_end'
-            m = f'The {step} should not return anything as of 9.1.' \
-                f'to log, use self.log(...) or self.write(...) directly in the LightningModule'
-            self.warning_cache.warn(m)
+            self.warning_cache.warn(
+                f'The {step} should not return anything as of 9.1.'
+                ' To log, use self.log(...) or self.write(...) directly in the LightningModule'
+            )
 
         if using_eval_result and not user_reduced:
             eval_results = self.__auto_reduce_result_objs(outputs)
diff --git a/tests/checkpointing/test_model_checkpoint.py b/tests/checkpointing/test_model_checkpoint.py
index c2b5b7e9fc8a92..d3d5f67bcfeaa3 100644
--- a/tests/checkpointing/test_model_checkpoint.py
+++ b/tests/checkpointing/test_model_checkpoint.py
@@ -100,7 +100,7 @@ def test_model_checkpoint_to_yaml(tmpdir, save_top_k):
     path_yaml = os.path.join(tmpdir, 'best_k_models.yaml')
     checkpoint.to_yaml(path_yaml)
     d = yaml.full_load(open(path_yaml, 'r'))
-    best_k = {k: v.item() for k, v in checkpoint.best_k_models.items()}
+    best_k = {k: v for k, v in checkpoint.best_k_models.items()}
     assert d == best_k
 
 
@@ -185,67 +185,72 @@ def test_model_checkpoint_no_extraneous_invocations(tmpdir):
 
 def test_model_checkpoint_format_checkpoint_name(tmpdir):
     # empty filename:
-    ckpt_name = ModelCheckpoint._format_checkpoint_name('', 3, {})
-    assert ckpt_name == 'epoch=3'
+    ckpt_name = ModelCheckpoint._format_checkpoint_name('', 3, 2, {})
+    assert ckpt_name == 'epoch=3-step=2'
 
-    ckpt_name = ModelCheckpoint._format_checkpoint_name(None, 3, {}, prefix='test')
-    assert ckpt_name == 'test-epoch=3'
+    ckpt_name = ModelCheckpoint._format_checkpoint_name(None, 3, 2, {}, prefix='test')
+    assert ckpt_name == 'test-epoch=3-step=2'
 
     # no groups case:
-    ckpt_name = ModelCheckpoint._format_checkpoint_name('ckpt', 3, {}, prefix='test')
+    ckpt_name = ModelCheckpoint._format_checkpoint_name('ckpt', 3, 2, {}, prefix='test')
     assert ckpt_name == 'test-ckpt'
 
     # no prefix
-    ckpt_name = ModelCheckpoint._format_checkpoint_name('{epoch:03d}-{acc}', 3, {'acc': 0.03})
+    ckpt_name = ModelCheckpoint._format_checkpoint_name('{epoch:03d}-{acc}', 3, 2, {'acc': 0.03})
     assert ckpt_name == 'epoch=003-acc=0.03'
 
     # prefix
     char_org = ModelCheckpoint.CHECKPOINT_JOIN_CHAR
     ModelCheckpoint.CHECKPOINT_JOIN_CHAR = '@'
-    ckpt_name = ModelCheckpoint._format_checkpoint_name('{epoch},{acc:.5f}', 3, {'acc': 0.03}, prefix='test')
+    ckpt_name = ModelCheckpoint._format_checkpoint_name('{epoch},{acc:.5f}', 3, 2, {'acc': 0.03}, prefix='test')
     assert ckpt_name == 'test@epoch=3,acc=0.03000'
     ModelCheckpoint.CHECKPOINT_JOIN_CHAR = char_org
 
     # no dirpath set
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath=None).format_checkpoint_name(3, {})
-    assert ckpt_name == 'epoch=3.ckpt'
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath='').format_checkpoint_name(5, {})
-    assert ckpt_name == 'epoch=5.ckpt'
+    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath=None).format_checkpoint_name(3, 2, {})
+    assert ckpt_name == 'epoch=3-step=2.ckpt'
+    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath='').format_checkpoint_name(5, 4, {})
+    assert ckpt_name == 'epoch=5-step=4.ckpt'
 
     # CWD
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath='.').format_checkpoint_name(3, {})
-    assert ckpt_name == str(Path('.').resolve() / 'epoch=3.ckpt')
+    ckpt_name = ModelCheckpoint(monitor='early_stop_on', dirpath='.').format_checkpoint_name(3, 4, {})
+    assert ckpt_name == str(Path('.').resolve() / 'epoch=3-step=4.ckpt')
 
     # with ver
     ckpt_name = ModelCheckpoint(
         monitor='early_stop_on', dirpath=tmpdir, filename='name', prefix='test'
-    ).format_checkpoint_name(3, {}, ver=3)
+    ).format_checkpoint_name(3, 2, {}, ver=3)
     assert ckpt_name == tmpdir / 'test-name-v3.ckpt'
 
     # using slashes
     ckpt_name = ModelCheckpoint(
         monitor='early_stop_on', dirpath=None, filename='{epoch}_{val/loss:.5f}'
-    ).format_checkpoint_name(4, {'val/loss': 0.03})
+    ).format_checkpoint_name(4, 3, {'val/loss': 0.03})
     assert ckpt_name == 'epoch=4_val/loss=0.03000.ckpt'
 
     # TODO: Checks with filepath. To be removed in v1.2
     # CWD
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', filepath='.').format_checkpoint_name(3, {})
-    assert ckpt_name == str(Path('.').resolve() / 'epoch=3.ckpt')
+    ckpt_name = ModelCheckpoint(monitor='early_stop_on', filepath='.').format_checkpoint_name(3, 2, {})
+    assert ckpt_name == str(Path('.').resolve() / 'epoch=3-step=2.ckpt')
 
     # dir does not exist so it is used as filename
     filepath = tmpdir / 'dir'
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', filepath=filepath, prefix='test').format_checkpoint_name(3, {})
+    ckpt_name = ModelCheckpoint(
+        monitor='early_stop_on', filepath=filepath, prefix='test'
+    ).format_checkpoint_name(3, 2, {})
     assert ckpt_name == tmpdir / 'test-dir.ckpt'
 
     # now, dir exists
     os.mkdir(filepath)
-    ckpt_name = ModelCheckpoint(monitor='early_stop_on', filepath=filepath, prefix='test').format_checkpoint_name(3, {})
-    assert ckpt_name == filepath / 'test-epoch=3.ckpt'
+    ckpt_name = ModelCheckpoint(
+        monitor='early_stop_on', filepath=filepath, prefix='test'
+    ).format_checkpoint_name(3, 2, {})
+    assert ckpt_name == filepath / 'test-epoch=3-step=2.ckpt'
 
 
 def test_model_checkpoint_save_last(tmpdir):
     """Tests that save_last produces only one last checkpoint."""
+    seed_everything()
     model = EvalModelTemplate()
     epochs = 3
     ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last-{epoch}'
@@ -257,10 +262,15 @@ def test_model_checkpoint_save_last(tmpdir):
         logger=False,
     )
     trainer.fit(model)
-    last_filename = model_checkpoint._format_checkpoint_name(ModelCheckpoint.CHECKPOINT_NAME_LAST, epochs - 1, {})
+    last_filename = model_checkpoint._format_checkpoint_name(
+        ModelCheckpoint.CHECKPOINT_NAME_LAST, trainer.current_epoch, trainer.global_step, {}
+    )
     last_filename = last_filename + '.ckpt'
     assert str(tmpdir / last_filename) == model_checkpoint.last_model_path
-    assert set(os.listdir(tmpdir)) == set([f'epoch={i}.ckpt' for i in range(epochs)] + [last_filename])
+    assert set(os.listdir(tmpdir)) == set(
+        [f"epoch={i}-step={j}.ckpt" for i, j in zip(range(epochs), [9, 19, 29])] + [last_filename]
+    )
+
     ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last'
 
 
@@ -295,6 +305,7 @@ def test_none_monitor_save_last(tmpdir):
 
 def test_model_checkpoint_none_monitor(tmpdir):
     """ Test that it is possible to save all checkpoints when monitor=None. """
+    seed_everything()
     model = EvalModelTemplate()
     model.validation_step = model.validation_step_no_monitor
     model.validation_epoch_end = model.validation_epoch_end_no_monitor
@@ -311,13 +322,13 @@ def test_model_checkpoint_none_monitor(tmpdir):
 
     # these should not be set if monitor is None
     assert checkpoint_callback.monitor is None
-    assert checkpoint_callback.best_model_path == checkpoint_callback.last_model_path == tmpdir / 'epoch=1.ckpt'
+    assert checkpoint_callback.best_model_path == checkpoint_callback.last_model_path == tmpdir / 'epoch=1-step=19.ckpt'
     assert checkpoint_callback.best_model_score == 0
     assert checkpoint_callback.best_k_models == {}
     assert checkpoint_callback.kth_best_model_path == ''
 
     # check that the correct ckpts were created
-    expected = [f'epoch={e}.ckpt' for e in range(epochs)]
+    expected = [f'epoch={i}-step={j}.ckpt' for i, j in zip(range(epochs), [9, 19])]
     assert set(os.listdir(tmpdir)) == set(expected)
 
 
@@ -325,13 +336,14 @@ def test_model_checkpoint_none_monitor(tmpdir):
 def test_model_checkpoint_period(tmpdir, period):
     model = EvalModelTemplate()
     epochs = 5
-    checkpoint_callback = ModelCheckpoint(dirpath=tmpdir, save_top_k=-1, period=period)
+    checkpoint_callback = ModelCheckpoint(dirpath=tmpdir, filename='{epoch}', save_top_k=-1, period=period)
     trainer = Trainer(
         default_root_dir=tmpdir,
         checkpoint_callback=checkpoint_callback,
         max_epochs=epochs,
         limit_train_batches=0.1,
         limit_val_batches=0.1,
+        val_check_interval=1.0,
         logger=False,
     )
     trainer.fit(model)
@@ -372,12 +384,19 @@ def validation_epoch_end(self, outputs):
             return {'epoch': self.current_epoch}
 
     model = CustomModel()
-    checkpoint_callback = ModelCheckpoint(dirpath=tmpdir, monitor="epoch", mode='max', save_top_k=-1)
+    checkpoint_callback = ModelCheckpoint(
+        dirpath=tmpdir,
+        filename="{epoch}",
+        monitor="epoch",
+        mode='max',
+        save_top_k=-1,
+    )
     trainer = Trainer(
         default_root_dir=tmpdir,
         checkpoint_callback=checkpoint_callback,
         max_epochs=epochs,
         logger=False,
+        val_check_interval=1.0,
     )
     trainer.fit(model)
 
@@ -439,7 +458,7 @@ def test_default_checkpoint_behavior(tmpdir):
     # make sure the checkpoint we saved has the metric in the name
     ckpts = os.listdir(os.path.join(tmpdir, 'lightning_logs', 'version_0', 'checkpoints'))
     assert len(ckpts) == 1
-    assert ckpts[0] == 'epoch=2.ckpt'
+    assert ckpts[0] == 'epoch=2-step=14.ckpt'
 
 
 def test_ckpt_metric_names_results(tmpdir):
@@ -497,7 +516,7 @@ def test_model_checkpoint_save_last_checkpoint_contents(tmpdir):
     model = EvalModelTemplate()
     num_epochs = 3
     model_checkpoint = ModelCheckpoint(
-        monitor='early_stop_on', dirpath=tmpdir, save_top_k=num_epochs, save_last=True
+        monitor='early_stop_on', dirpath=tmpdir, filename="{epoch}", save_top_k=num_epochs, save_last=True
     )
     trainer = Trainer(
         default_root_dir=tmpdir,
@@ -509,6 +528,7 @@ def test_model_checkpoint_save_last_checkpoint_contents(tmpdir):
     path_last_epoch = str(tmpdir / f"epoch={num_epochs - 1}.ckpt")
     path_last = str(tmpdir / "last.ckpt")
     assert path_last == model_checkpoint.last_model_path
+    assert os.path.isfile(path_last_epoch)
 
     ckpt_last_epoch = torch.load(path_last_epoch)
     ckpt_last = torch.load(path_last)
@@ -791,3 +811,25 @@ def test_configure_model_checkpoint(tmpdir):
 
     with pytest.raises(MisconfigurationException, match="checkpoint_callback=False but found ModelCheckpoint"):
         Trainer(checkpoint_callback=False, callbacks=[callback1], **kwargs)
+
+
+def test_val_check_interval_checkpoint_files(tmpdir):
+    """ Test correct checkpoint naming when validating/checkpointing multiple times per epoch. """
+    model = EvalModelTemplate()
+    model_checkpoint = ModelCheckpoint(
+        dirpath=tmpdir,
+        save_top_k=-1,
+        monitor="val_acc",
+        mode="max",
+        verbose=True
+    )
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        val_check_interval=0.2,
+        max_epochs=1,
+        limit_train_batches=10,
+        callbacks=[model_checkpoint]
+    )
+    trainer.fit(model)
+    files = sorted([p.name for p in Path(tmpdir).glob("*.ckpt")])
+    assert files == [f"epoch=0-step={s}.ckpt" for s in [1, 3, 5, 7, 9]]
diff --git a/tests/loggers/test_comet.py b/tests/loggers/test_comet.py
index 87af510e492194..fc61829645b6e3 100644
--- a/tests/loggers/test_comet.py
+++ b/tests/loggers/test_comet.py
@@ -159,7 +159,7 @@ def test_comet_logger_dirs_creation(comet, comet_experiment, tmpdir, monkeypatch
     trainer.fit(model)
 
     assert trainer.checkpoint_callback.dirpath == (tmpdir / 'test' / "1" / 'checkpoints')
-    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0.ckpt'}
+    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0-step=9.ckpt'}
 
 
 @patch('pytorch_lightning.loggers.comet.comet_ml')
diff --git a/tests/loggers/test_mlflow.py b/tests/loggers/test_mlflow.py
index db2c353dc4e2c6..a200fbf549e6a1 100644
--- a/tests/loggers/test_mlflow.py
+++ b/tests/loggers/test_mlflow.py
@@ -115,7 +115,7 @@ def test_mlflow_log_dir(client, mlflow, tmpdir):
     )
     trainer.fit(model)
     assert trainer.checkpoint_callback.dirpath == (tmpdir / "exp-id" / "run-id" / 'checkpoints')
-    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0.ckpt'}
+    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0-step=0.ckpt'}
 
 
 def test_mlflow_logger_dirs_creation(tmpdir):
@@ -143,7 +143,7 @@ def test_mlflow_logger_dirs_creation(tmpdir):
     assert 'epoch' in os.listdir(tmpdir / exp_id / run_id / 'metrics')
     assert set(os.listdir(tmpdir / exp_id / run_id / 'params')) == model.hparams.keys()
     assert trainer.checkpoint_callback.dirpath == (tmpdir / exp_id / run_id / 'checkpoints')
-    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0.ckpt'}
+    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0-step=9.ckpt'}
 
 
 @mock.patch('pytorch_lightning.loggers.mlflow.mlflow')
diff --git a/tests/loggers/test_wandb.py b/tests/loggers/test_wandb.py
index a7fd986bad642f..468ca819f91b18 100644
--- a/tests/loggers/test_wandb.py
+++ b/tests/loggers/test_wandb.py
@@ -116,7 +116,7 @@ def test_wandb_logger_dirs_creation(wandb, tmpdir):
     trainer.fit(model)
 
     assert trainer.checkpoint_callback.dirpath == str(tmpdir / 'project' / version / 'checkpoints')
-    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0.ckpt'}
+    assert set(os.listdir(trainer.checkpoint_callback.dirpath)) == {'epoch=0-step=9.ckpt'}
 
 
 def test_wandb_sanitize_callable_params(tmpdir):
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index 35257e28704ba0..6fceae4b5e59d9 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -430,7 +430,7 @@ def mock_save_function(filepath, *args):
     losses = [10, 9, 2.8, 5, 2.5]
 
     checkpoint_callback = ModelCheckpoint(
-        dirpath=tmpdir, monitor='checkpoint_on', save_top_k=save_top_k,
+        dirpath=tmpdir, filename='{epoch}', monitor='checkpoint_on', save_top_k=save_top_k,
         save_last=save_last, prefix=file_prefix, verbose=1
     )
     checkpoint_callback.save_function = mock_save_function