diff --git a/docs/source/common/trainer.rst b/docs/source/common/trainer.rst
index 9fde434e78579..de37f5839e82b 100644
--- a/docs/source/common/trainer.rst
+++ b/docs/source/common/trainer.rst
@@ -907,6 +907,9 @@ Stop training once this number of epochs is reached
     # default used by the Trainer
     trainer = Trainer(max_epochs=1000)
 
+If both ``max_epochs`` and ``max_steps`` aren't specified, ``max_epochs`` will default to ``1000``.
+To enable infinite training, set ``max_epochs = -1``.
+
 min_epochs
 ^^^^^^^^^^
 
@@ -947,6 +950,9 @@ Training will stop if max_steps or max_epochs have reached (earliest).
     # Stop after 100 steps
     trainer = Trainer(max_steps=100)
 
+If ``max_steps`` is not specified, ``max_epochs`` will be used instead (and ``max_epochs`` defaults to
+``1000`` if ``max_epochs`` is not specified). To disable this default, set ``max_steps = -1``.
+
 min_steps
 ^^^^^^^^^
 
diff --git a/pytorch_lightning/loops/epoch/training_epoch_loop.py b/pytorch_lightning/loops/epoch/training_epoch_loop.py
index 2020ac6cc6564..93628e5114ec5 100644
--- a/pytorch_lightning/loops/epoch/training_epoch_loop.py
+++ b/pytorch_lightning/loops/epoch/training_epoch_loop.py
@@ -37,6 +37,9 @@ class TrainingEpochLoop(loops.Loop):
     def __init__(self, min_steps: int, max_steps: int):
         super().__init__()
         self.min_steps: int = min_steps
+
+        if max_steps and max_steps < -1:
+            raise MisconfigurationException(f"`max_steps` must be a positive integer or -1. You passed in {max_steps}.")
         self.max_steps: int = max_steps
 
         self.global_step: int = 0
diff --git a/pytorch_lightning/loops/fit_loop.py b/pytorch_lightning/loops/fit_loop.py
index 47eb50a2ab100..c7d5dad492bef 100644
--- a/pytorch_lightning/loops/fit_loop.py
+++ b/pytorch_lightning/loops/fit_loop.py
@@ -20,6 +20,7 @@
 from pytorch_lightning.trainer.connectors.logger_connector.result import ResultCollection
 from pytorch_lightning.trainer.progress import Progress
 from pytorch_lightning.trainer.supporters import TensorRunningAccum
+from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 log = logging.getLogger(__name__)
 
@@ -35,6 +36,12 @@ class FitLoop(Loop):
 
     def __init__(self, min_epochs: Optional[int] = None, max_epochs: Optional[int] = None):
         super().__init__()
+        # Allow max_epochs or max_steps to be zero, since this will be handled by fit_loop.done
+        if max_epochs and max_epochs < -1:
+            raise MisconfigurationException(
+                f"`max_epochs` must be a positive integer or -1. You passed in {max_epochs}."
+            )
+
         self.max_epochs = max_epochs
         self.min_epochs = min_epochs
         self.epoch_loop: Optional[TrainingEpochLoop] = None
@@ -98,6 +105,8 @@ def max_steps(self) -> int:
     def max_steps(self, value: int) -> None:
         """Sets the maximum number of steps (forwards to epoch_loop)"""
         # TODO(@awaelchli): This setter is required by debugging connector (fast dev run), should be avoided
+        if value and value < -1:
+            raise MisconfigurationException(f"`max_steps` must be a positive integer or -1. You passed in {value}.")
         self.epoch_loop.max_steps = value
 
     @property
@@ -123,6 +132,19 @@ def _results(self) -> ResultCollection:
             return self.epoch_loop.val_loop._results
         raise RuntimeError("`FitLoop._results` property isn't defined. Accessed outside of scope")
 
+    @staticmethod
+    def _is_max_limit_enabled(max_value: Optional[int]) -> bool:
+        """Checks whether the max_value is enabled. This can
+        be used for checking whether max_epochs or max_steps is enabled.
+
+        Args:
+            max_value: the value to check
+
+        Returns:
+            whether the limit for this value should be enabled
+        """
+        return max_value not in (None, -1)
+
     @property
     def done(self) -> bool:
         """Evaluates when to leave the loop.
@@ -131,8 +153,8 @@ def done(self) -> bool:
         or if the maximum number of steps or epochs is reached.
         """
         # TODO(@awaelchli): Move track steps inside training loop and move part of these condition inside training loop
-        stop_steps = self.max_steps is not None and self.global_step >= self.max_steps
-        stop_epochs = self.max_epochs is not None and self.current_epoch >= self.max_epochs
+        stop_steps = FitLoop._is_max_limit_enabled(self.max_steps) and self.global_step >= self.max_steps
+        stop_epochs = FitLoop._is_max_limit_enabled(self.max_epochs) and self.current_epoch >= self.max_epochs
 
         should_stop = False
         if self.trainer.should_stop:
diff --git a/pytorch_lightning/trainer/connectors/checkpoint_connector.py b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
index 73002dc1b9325..ce119d80c24eb 100644
--- a/pytorch_lightning/trainer/connectors/checkpoint_connector.py
+++ b/pytorch_lightning/trainer/connectors/checkpoint_connector.py
@@ -21,6 +21,7 @@
 from torchmetrics import Metric
 
 import pytorch_lightning as pl
+from pytorch_lightning.loops.fit_loop import FitLoop
 from pytorch_lightning.utilities import _OMEGACONF_AVAILABLE, rank_zero_deprecation, rank_zero_info, rank_zero_warn
 from pytorch_lightning.utilities.cloud_io import atomic_save, get_filesystem
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
@@ -190,7 +191,10 @@ def restore_loops(self) -> None:
         self.trainer.fit_loop.current_epoch = self._loaded_checkpoint["epoch"]
 
         # crash if max_epochs is lower then the current epoch from the checkpoint
-        if self.trainer.max_epochs is not None and self.trainer.current_epoch > self.trainer.max_epochs:
+        if (
+            FitLoop._is_max_limit_enabled(self.trainer.max_epochs)
+            and self.trainer.current_epoch > self.trainer.max_epochs
+        ):
             raise MisconfigurationException(
                 f"You restored a checkpoint with current_epoch={self.trainer.current_epoch},"
                 f" but you have set Trainer(max_epochs={self.trainer.max_epochs})."
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 3e84c725b9663..d19d38efed522 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -268,12 +268,15 @@ def __init__(
                 Can be used on CPU, GPU or TPUs.
 
             max_epochs: Stop training once this number of epochs is reached. Disabled by default (None).
-                If both max_epochs and max_steps are not specified, defaults to ``max_epochs`` = 1000.
+                If both max_epochs and max_steps are not specified, defaults to ``max_epochs = 1000``.
+                To enable infinite training, set ``max_epochs = -1``.
 
             min_epochs: Force training for at least these many epochs. Disabled by default (None).
-                If both min_epochs and min_steps are not specified, defaults to ``min_epochs`` = 1.
+                If both min_epochs and min_steps are not specified, defaults to ``min_epochs = 1``.
 
-            max_steps: Stop training after this number of steps. Disabled by default (None).
+            max_steps: Stop training after this number of steps. Disabled by default (None). If ``max_steps = None``
+                and ``max_epochs = None``, will default to ``max_epochs = 1000``. To disable this default, set
+                ``max_steps`` to ``-1``.
 
             min_steps: Force training for at least these number of steps. Disabled by default (None).
 
@@ -380,6 +383,7 @@ def __init__(
         self.slurm_connector = SLURMConnector(self)
         self.tuner = Tuner(self)
 
+        # max_epochs won't default to 1000 if max_steps/max_time are specified (including being set to -1).
         fit_loop = FitLoop(
             min_epochs=(1 if (min_epochs is None and min_steps is None and max_time is None) else min_epochs),
             max_epochs=(1000 if (max_epochs is None and max_steps is None and max_time is None) else max_epochs),
diff --git a/tests/callbacks/test_timer.py b/tests/callbacks/test_timer.py
index c7b636d3f843a..92643ba51b82c 100644
--- a/tests/callbacks/test_timer.py
+++ b/tests/callbacks/test_timer.py
@@ -42,9 +42,13 @@ def on_fit_start(self):
         trainer.fit(TestModel())
     assert "callbacks list already contains a Timer" in caplog.text
 
-    seconds = 1
-    trainer = Trainer(max_time=dict(seconds=seconds))
-    assert trainer.max_epochs is None
+    # Make sure max_time still honored even if max_epochs == -1
+    trainer = Trainer(max_time=dict(seconds=1), max_epochs=-1)
+    with pytest.raises(SystemExit):
+        trainer.fit(TestModel())
+    timer = [c for c in trainer.callbacks if isinstance(c, Timer)][0]
+    assert timer._duration == 1
+    assert trainer.max_epochs == -1
     assert trainer.max_steps is None
 
 
@@ -153,7 +157,11 @@ def test_timer_resume_training(tmpdir):
     checkpoint_callback = ModelCheckpoint(dirpath=tmpdir, save_top_k=-1)
 
     # initial training
-    trainer = Trainer(default_root_dir=tmpdir, max_epochs=100, callbacks=[timer, checkpoint_callback])
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        max_epochs=100,
+        callbacks=[timer, checkpoint_callback],
+    )
     trainer.fit(model)
     assert not timer._offset
     assert timer.time_remaining() <= 0
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index 9a58351ecaaf5..90b5847fc0057 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -33,7 +33,7 @@
 
 import tests.helpers.utils as tutils
 from pytorch_lightning import Callback, LightningDataModule, LightningModule, Trainer
-from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
+from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint, Timer
 from pytorch_lightning.callbacks.prediction_writer import BasePredictionWriter
 from pytorch_lightning.core.saving import load_hparams_from_tags_csv, load_hparams_from_yaml, save_hparams_to_tags_csv
 from pytorch_lightning.loggers import TensorBoardLogger
@@ -492,6 +492,57 @@ def test_trainer_max_steps_and_epochs(tmpdir):
     assert trainer.global_step == num_train_samples * trainer.max_epochs
     assert trainer.current_epoch == trainer.max_epochs - 1, "Model did not stop at max_epochs"
 
+    # if max_steps is positive and max_epochs is negative, use max_steps
+    trainer_kwargs["max_epochs"] = -1
+    trainer_kwargs["max_steps"] = 3
+    trainer = Trainer(**trainer_kwargs)
+    trainer.fit(model)
+
+    assert trainer.state.finished, f"Training failed with {trainer.state}"
+    assert trainer.global_step == 3
+
+
+@pytest.mark.parametrize(
+    "max_epochs,max_steps,incorrect_variable,incorrect_value",
+    [
+        (-100, None, "max_epochs", -100),
+        (1, -2, "max_steps", -2),
+    ],
+)
+def test_trainer_max_steps_and_epochs_validation(max_epochs, max_steps, incorrect_variable, incorrect_value):
+    """Don't allow max_epochs or max_steps to be less than -1 or a float"""
+    with pytest.raises(
+        MisconfigurationException,
+        match=f"`{incorrect_variable}` must be a positive integer or -1. You passed in {incorrect_value}",
+    ):
+        Trainer(max_epochs=max_epochs, max_steps=max_steps)
+
+
+@pytest.mark.parametrize(
+    "max_epochs,max_steps,is_done,correct_trainer_epochs",
+    [
+        (None, None, False, 1000),
+        (-1, None, False, -1),
+        (None, -1, False, None),
+        (5, -1, False, 5),
+        (-1, 10, False, -1),
+        (None, 0, True, None),
+        (0, None, True, 0),
+        (-1, 0, True, -1),
+        (0, -1, True, 0),
+    ],
+)
+def test_trainer_max_steps_and_epochs_fit_loop_done(max_epochs, max_steps, is_done, correct_trainer_epochs):
+    trainer = Trainer(max_epochs=max_epochs, max_steps=max_steps)
+
+    assert trainer.max_epochs == correct_trainer_epochs
+    assert trainer.max_steps == max_steps
+    assert trainer.fit_loop.done is is_done
+
+    # Make sure there is no timer
+    timer_callbacks = [c for c in trainer.callbacks if isinstance(c, Timer)]
+    assert len(timer_callbacks) == 0
+
 
 def test_trainer_min_steps_and_epochs(tmpdir):
     """Verify model trains according to specified min steps"""