diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5a10d80b91678..97f5f038970c7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 ### Added
 
 
+- Added support for `log_model=best_and_last` option in `pytorch_lightning.loggers.WandbLogger`.
+
+
 - Register `ShardedTensor` state dict hooks in `LightningModule.__init__` if the pytorch version supports `ShardedTensor` ([#8944](https://github.com/PyTorchLightning/pytorch-lightning/pull/8944))
 
 
diff --git a/pytorch_lightning/loggers/wandb.py b/pytorch_lightning/loggers/wandb.py
index c93b8d02bca16..8b19097044ae2 100644
--- a/pytorch_lightning/loggers/wandb.py
+++ b/pytorch_lightning/loggers/wandb.py
@@ -64,6 +64,8 @@ class WandbLogger(LightningLoggerBase):
             as W&B artifacts.
 
             * if ``log_model == 'all'``, checkpoints are logged during training.
+            * if ``log_model == 'best_and_last'``, checkpoints are logged during training and only the best and the
+              last checkpoints (according to ModelCheckpoint) are kept as wandb artifacts. Previous versions are automatically deleted.
             * if ``log_model == True``, checkpoints are logged at the end of training, except when
               :paramref:`~pytorch_lightning.callbacks.model_checkpoint.ModelCheckpoint.save_top_k` ``== -1``
               which also logs every checkpoint during training.
@@ -248,7 +250,11 @@ def version(self) -> Optional[str]:
 
     def after_save_checkpoint(self, checkpoint_callback: "ReferenceType[ModelCheckpoint]") -> None:
         # log checkpoints as artifacts
-        if self._log_model == "all" or self._log_model is True and checkpoint_callback.save_top_k == -1:
+        if (
+            self._log_model == "all"
+            or (self._log_model is True and checkpoint_callback.save_top_k == -1)
+            or self._log_model == "best_and_last"
+        ):
             self._scan_and_log_checkpoints(checkpoint_callback)
         elif self._log_model is True:
             self._checkpoint_callback = checkpoint_callback
@@ -301,3 +307,13 @@ def _scan_and_log_checkpoints(self, checkpoint_callback: "ReferenceType[ModelChe
             self.experiment.log_artifact(artifact, aliases=aliases)
             # remember logged models - timestamp needed in case filename didn't change (lastkckpt or custom name)
             self._logged_model_time[p] = t
+
+        if self._log_model == "best_and_last":
+            # Clean up previous artifacts.
+            # Adapted from https://gitbook-docs.wandb.ai/guides/artifacts/api#cleaning-up-unused-versions
+            api = wandb.Api(overrides={"project": self.experiment.project})
+
+            for version in api.artifact_versions(f"model-{self.experiment.id}", "model"):
+                # Clean up all versions that don't have an alias such as 'latest'.
+                if len(version.aliases) == 0:
+                    version.delete()
diff --git a/tests/loggers/test_wandb.py b/tests/loggers/test_wandb.py
index 8388d7877ab7e..bf33c1a974fc7 100644
--- a/tests/loggers/test_wandb.py
+++ b/tests/loggers/test_wandb.py
@@ -176,6 +176,16 @@ def test_wandb_log_model(wandb, tmpdir):
     trainer.fit(model)
     assert wandb.init().log_artifact.call_count == 2
 
+    # test log_model='best_and_last'
+    wandb.init().log_artifact.reset_mock()
+    wandb.init.reset_mock()
+    logger = WandbLogger(log_model="best_and_last")
+    logger.experiment.id = "1"
+    logger.experiment.project_name.return_value = "project"
+    trainer = Trainer(default_root_dir=tmpdir, logger=logger, max_epochs=2, limit_train_batches=3, limit_val_batches=3)
+    trainer.fit(model)
+    assert wandb.init().log_artifact.call_count == 2
+
     # test log_model=False
     wandb.init().log_artifact.reset_mock()
     wandb.init.reset_mock()
@@ -203,7 +213,7 @@ def test_wandb_log_model(wandb, tmpdir):
         type="model",
         metadata={
             "score": None,
-            "original_filename": "epoch=1-step=5-v3.ckpt",
+            "original_filename": "epoch=1-step=5-v4.ckpt",
             "ModelCheckpoint": {
                 "monitor": None,
                 "mode": "min",
diff --git a/tests/trainer/loops/test_training_loop.py b/tests/trainer/loops/test_training_loop.py
index c37681e4831ca..d21e8efc7a5cb 100644
--- a/tests/trainer/loops/test_training_loop.py
+++ b/tests/trainer/loops/test_training_loop.py
@@ -191,7 +191,7 @@ def training_epoch_end(self, outputs) -> None:
 
 
 def test_batch_loop_releases_loss(tmpdir):
-    """Test that loss/graph is released so that it can be garbage collected before the next training step"""
+    """Test that loss/graph is released so that it can be garbage collected before the next training step."""
 
     class TestModel(BoringModel):
         def training_step(self, batch, batch_idx):