diff --git a/pytorch_lightning/callbacks/quantization.py b/pytorch_lightning/callbacks/quantization.py
index ca82a574f71d1..42f0d575ffb6f 100644
--- a/pytorch_lightning/callbacks/quantization.py
+++ b/pytorch_lightning/callbacks/quantization.py
@@ -28,7 +28,7 @@
 if _TORCH_GREATER_EQUAL_1_8:
     from torch.quantization import FakeQuantizeBase
 else:
-    # For torch 1.6 and 1.7.
+    # For torch 1.7.
     from torch.quantization import FakeQuantize as FakeQuantizeBase
 
 import pytorch_lightning as pl
diff --git a/pytorch_lightning/distributed/dist.py b/pytorch_lightning/distributed/dist.py
index 082e0c617a5f7..a0054d17936b0 100644
--- a/pytorch_lightning/distributed/dist.py
+++ b/pytorch_lightning/distributed/dist.py
@@ -13,7 +13,8 @@
 # limitations under the License.
 from typing import Any
 
-from pytorch_lightning.overrides.torch_distributed import broadcast_object_list
+import torch.distributed
+
 from pytorch_lightning.utilities import rank_zero_deprecation
 from pytorch_lightning.utilities.distributed import group as _group
 
@@ -40,6 +41,6 @@ def broadcast(self, obj: Any, group=_group.WORLD):
         if self.rank != 0:
             obj = [None] * len(obj)
 
-        broadcast_object_list(obj, 0, group=group or _group.WORLD)
+        torch.distributed.broadcast_object_list(obj, 0, group=group or _group.WORLD)
 
         return obj[0]
diff --git a/pytorch_lightning/overrides/torch_distributed.py b/pytorch_lightning/overrides/torch_distributed.py
deleted file mode 100644
index 3cbbe5ea760ff..0000000000000
--- a/pytorch_lightning/overrides/torch_distributed.py
+++ /dev/null
@@ -1,99 +0,0 @@
-import logging
-import pickle
-
-import torch
-
-from pytorch_lightning.utilities.imports import _TORCH_GREATER_EQUAL_1_8
-
-log = logging.getLogger(__name__)
-
-if torch.distributed.is_available():
-    from torch.distributed import Backend, broadcast, get_backend, get_rank, GroupMember
-
-# The code underneath is taken from PyTorch `torch/distributed/distributed_c10d.py`
-# and enable broadcasting for PyTorch 1.6 and lower.
-
-
-# https://github.com/pytorch/pytorch/blob/1.7/torch/distributed/distributed_c10d.py#L160
-def _rank_not_in_group(group):
-    """Helper that checks if the current process's rank is not in a given group."""
-    if group is None:
-        return False
-    return group == GroupMember.NON_GROUP_MEMBER
-
-
-# Taken from https://github.com/pytorch/pytorch/blob/1.7/torch/distributed/distributed_c10d.py#L1164
-def _object_to_tensor(obj):
-    buffer = pickle.dumps(obj)
-    byte_storage = torch.ByteStorage.from_buffer(buffer)  # type: ignore[attr-defined]
-    byte_tensor = torch.ByteTensor(byte_storage)
-    local_size = torch.LongTensor([byte_tensor.numel()])
-    return byte_tensor, local_size
-
-
-# Taken from https://github.com/pytorch/pytorch/blob/1.7/torch/distributed/distributed_c10d.py
-def _tensor_to_object(tensor, tensor_size):
-    buf = tensor.numpy().tobytes()[:tensor_size]
-    out = pickle.loads(buf)
-    return out
-
-
-# Taken from https://github.com/pytorch/pytorch/blob/1.7/torch/distributed/distributed_c10d.py#L1327
-def _broadcast_object_list(object_list, src=0, group=None):
-    if _rank_not_in_group(group):
-        return
-
-    my_rank = get_rank()
-    # Serialize object_list elements to tensors on src rank.
-    if my_rank == src:
-        tensor_list, size_list = zip(*(_object_to_tensor(obj) for obj in object_list))
-        object_sizes_tensor = torch.cat(size_list)
-    else:
-        object_sizes_tensor = torch.LongTensor(len(object_list))
-
-    group_backend = get_backend(group)
-    is_nccl_backend = group_backend == Backend.NCCL
-    current_device = torch.device("cpu")
-    if is_nccl_backend:
-        # See note about using torch.cuda.current_device() here in docstring.
-        # We cannot simply use my_rank since rank == device is not necessarily
-        # true.
-        current_device = torch.device("cuda", torch.cuda.current_device())
-        object_sizes_tensor = object_sizes_tensor.to(current_device)
-        object_sizes_tensor = object_sizes_tensor.to(current_device)
-
-    # Broadcast object sizes
-    broadcast(object_sizes_tensor, src=src, group=group)
-
-    # Concatenate and broadcast serialized object tensors
-    if my_rank == src:
-        object_tensor = torch.cat(tensor_list)
-    else:
-        object_tensor = torch.ByteTensor(torch.sum(object_sizes_tensor).item())
-
-    if is_nccl_backend:
-        object_tensor = object_tensor.to(current_device)
-
-    broadcast(object_tensor, src=src, group=group)
-
-    # Deserialize objects using their stored sizes.
-    offset = 0
-    if my_rank != src:
-        for i, obj_size in enumerate(object_sizes_tensor):
-            obj_view = object_tensor[offset : offset + obj_size]
-            obj_view = obj_view.type(torch.ByteTensor)  # type: ignore[call-overload]
-            offset += obj_size
-            object_list[i] = _tensor_to_object(obj_view, obj_size)
-
-
-if not torch.distributed.is_available():
-    # avoid failures on early PyTorch versions for Windows where
-    # not all functions used in `broadcast_object_list` are available.
-    def _broadcast_noop(obj, *_, **__):
-        return obj
-
-    broadcast_object_list = _broadcast_noop
-elif _TORCH_GREATER_EQUAL_1_8:
-    from torch.distributed.distributed_c10d import broadcast_object_list
-else:
-    broadcast_object_list = _broadcast_object_list
diff --git a/pytorch_lightning/plugins/training_type/ddp.py b/pytorch_lightning/plugins/training_type/ddp.py
index c528be4c8bfef..84e9b55b9ee08 100644
--- a/pytorch_lightning/plugins/training_type/ddp.py
+++ b/pytorch_lightning/plugins/training_type/ddp.py
@@ -34,7 +34,6 @@
 from pytorch_lightning.core.optimizer import LightningOptimizer
 from pytorch_lightning.overrides import LightningDistributedModule
 from pytorch_lightning.overrides.distributed import prepare_for_backward
-from pytorch_lightning.overrides.torch_distributed import broadcast_object_list
 from pytorch_lightning.plugins.environments.cluster_environment import ClusterEnvironment
 from pytorch_lightning.plugins.io.checkpoint_plugin import CheckpointIO
 from pytorch_lightning.plugins.training_type.parallel import ParallelPlugin
@@ -43,7 +42,6 @@
     _FAIRSCALE_AVAILABLE,
     _HYDRA_AVAILABLE,
     _IS_WINDOWS,
-    _TORCH_GREATER_EQUAL_1_7,
     _TORCH_GREATER_EQUAL_1_8,
     _TORCH_GREATER_EQUAL_1_9,
     _TORCH_GREATER_EQUAL_1_10,
@@ -255,15 +253,13 @@ def pre_configure_ddp(self):
         # when not all parameter backward hooks are fired by the autograd engine even if require_grad is set to True.
         # This flag does come with a performance hit, so it is suggested to disable in cases where it is possible.
         self._ddp_kwargs["find_unused_parameters"] = self._ddp_kwargs.get("find_unused_parameters", True)
-        # todo: PyTorch 1.7.0 DDP introduces `self.reducer._rebuild_buckets()` breaking manual_optimization
-        if (
-            _TORCH_GREATER_EQUAL_1_7
-            and not self.lightning_module.automatic_optimization
-            and not self._ddp_kwargs.get("find_unused_parameters", False)
+        if not self.lightning_module.automatic_optimization and not self._ddp_kwargs.get(
+            "find_unused_parameters", False
         ):
+            # TODO: PyTorch 1.7.0 DDP introduces `self.reducer._rebuild_buckets()` breaking manual_optimization
             rank_zero_warn(
-                "From PyTorch 1.7.0, Lightning ``manual_optimization`` needs to set ``find_unused_parameters=True`` "
-                "to properly work with DDP."
+                "From PyTorch 1.7.0, Lightning `manual_optimization` needs to set `find_unused_parameters=True` to"
+                " properly work with DDP. Using `find_unused_parameters=True`."
             )
             self._ddp_kwargs["find_unused_parameters"] = True
 
@@ -371,7 +367,7 @@ def broadcast(self, obj: object, src: int = 0) -> object:
         obj = [obj]
         if self.global_rank != src:
             obj = [None]
-        broadcast_object_list(obj, src, group=_group.WORLD)
+        torch.distributed.broadcast_object_list(obj, src, group=_group.WORLD)
         return obj[0]
 
     def pre_backward(self, closure_loss: torch.Tensor) -> None:
diff --git a/pytorch_lightning/plugins/training_type/ddp_spawn.py b/pytorch_lightning/plugins/training_type/ddp_spawn.py
index 926409925b9c7..677e031cd04af 100644
--- a/pytorch_lightning/plugins/training_type/ddp_spawn.py
+++ b/pytorch_lightning/plugins/training_type/ddp_spawn.py
@@ -27,12 +27,11 @@
 import pytorch_lightning as pl
 from pytorch_lightning.overrides import LightningDistributedModule
 from pytorch_lightning.overrides.distributed import prepare_for_backward
-from pytorch_lightning.overrides.torch_distributed import broadcast_object_list
 from pytorch_lightning.plugins.environments.cluster_environment import ClusterEnvironment
 from pytorch_lightning.plugins.io.checkpoint_plugin import CheckpointIO
 from pytorch_lightning.plugins.training_type.parallel import ParallelPlugin
 from pytorch_lightning.trainer.states import TrainerFn
-from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_7, _TORCH_GREATER_EQUAL_1_8, rank_zero_warn
+from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_8, rank_zero_warn
 from pytorch_lightning.utilities.apply_func import apply_to_collection, move_data_to_device
 from pytorch_lightning.utilities.cloud_io import atomic_save
 from pytorch_lightning.utilities.cloud_io import load as pl_load
@@ -238,15 +237,13 @@ def pre_configure_ddp(self):
         # when not all parameter backward hooks are fired by the autograd engine even if require_grad is set to True.
         # This flag does come with a performance hit, so it is suggested to disable in cases where it is possible.
         self._ddp_kwargs["find_unused_parameters"] = self._ddp_kwargs.get("find_unused_parameters", True)
-        # todo: PyTorch 1.7.0 DDP introduces `self.reducer._rebuild_buckets()` breaking manual_optimization
-        if (
-            _TORCH_GREATER_EQUAL_1_7
-            and not self.lightning_module.automatic_optimization
-            and not self._ddp_kwargs.get("find_unused_parameters", False)
+        if not self.lightning_module.automatic_optimization and not self._ddp_kwargs.get(
+            "find_unused_parameters", False
         ):
+            # TODO: PyTorch 1.7.0 DDP introduces `self.reducer._rebuild_buckets()` breaking manual_optimization
             rank_zero_warn(
-                "From PyTorch 1.7.0, Lightning ``manual_optimization`` needs to set ``find_unused_parameters=True`` "
-                "to properly work with DDP."
+                "From PyTorch 1.7.0, Lightning `manual_optimization` needs to set `find_unused_parameters=True` to"
+                " properly work with DDP. Using `find_unused_parameters=True`."
             )
             self._ddp_kwargs["find_unused_parameters"] = True
 
@@ -323,7 +320,7 @@ def broadcast(self, obj: object, src: int = 0) -> object:
         obj = [obj]
         if self.global_rank != src:
             obj = [None]
-        broadcast_object_list(obj, src, group=_group.WORLD)
+        torch.distributed.broadcast_object_list(obj, src, group=_group.WORLD)
         return obj[0]
 
     def model_to_device(self):
diff --git a/pytorch_lightning/trainer/connectors/accelerator_connector.py b/pytorch_lightning/trainer/connectors/accelerator_connector.py
index e15f7bb853db8..43eb65ce21a22 100644
--- a/pytorch_lightning/trainer/connectors/accelerator_connector.py
+++ b/pytorch_lightning/trainer/connectors/accelerator_connector.py
@@ -74,7 +74,6 @@
 from pytorch_lightning.utilities.imports import (
     _HOROVOD_AVAILABLE,
     _IPU_AVAILABLE,
-    _TORCH_GREATER_EQUAL_1_7,
     _TORCH_GREATER_EQUAL_1_8,
     _TPU_AVAILABLE,
 )
@@ -190,10 +189,8 @@ def _init_deterministic(self, deterministic: bool) -> None:
         self.deterministic = deterministic
         if _TORCH_GREATER_EQUAL_1_8:
             torch.use_deterministic_algorithms(deterministic)
-        elif _TORCH_GREATER_EQUAL_1_7:
+        else:
             torch.set_deterministic(deterministic)
-        else:  # the minimum version Lightning supports is PyTorch 1.6
-            torch._set_deterministic(deterministic)
         if deterministic:
             # fixing non-deterministic part of horovod
             # https://github.com/PyTorchLightning/pytorch-lightning/pull/1572/files#r420279383
diff --git a/pytorch_lightning/utilities/__init__.py b/pytorch_lightning/utilities/__init__.py
index 158d7356c91ce..7343e28d6d811 100644
--- a/pytorch_lightning/utilities/__init__.py
+++ b/pytorch_lightning/utilities/__init__.py
@@ -44,7 +44,6 @@
     _OMEGACONF_AVAILABLE,
     _POPTORCH_AVAILABLE,
     _RICH_AVAILABLE,
-    _TORCH_GREATER_EQUAL_1_7,
     _TORCH_GREATER_EQUAL_1_8,
     _TORCH_GREATER_EQUAL_1_9,
     _TORCH_GREATER_EQUAL_1_10,
diff --git a/pytorch_lightning/utilities/auto_restart.py b/pytorch_lightning/utilities/auto_restart.py
index f0b50103cf2f2..ef52717636d90 100644
--- a/pytorch_lightning/utilities/auto_restart.py
+++ b/pytorch_lightning/utilities/auto_restart.py
@@ -305,9 +305,6 @@ def _wrap_generator_samplers(self) -> None:
         # access wrapped dataset attributes
         dataset_dict = self.dataset.__dict__
 
-        # create a tuple of sampler names
-        samplers_names = tuple(v.__class__.__name__ for k, v in dataset_dict.items() if isinstance(v, Sampler))
-
         # create a dictionary of generator present within the dataset attributes
         dataset_sampler_generators = {k: v for k, v in dataset_dict.items() if isinstance(v, (Generator, Iterator))}
 
@@ -318,31 +315,17 @@ def _wrap_generator_samplers(self) -> None:
             if isinstance(generator, Sampler):
                 continue
 
-            # used to handle a weird behaviour from PyTorch 1.6
-            # where the sampler is converted to a list_iterator
-            is_legacy = False
-
-            if isinstance(generator, Generator):
-                # Generator name have the  the form `SamplerName.__iter__`
-                generator_name = generator.__qualname__.split(".")[0]
-            else:
-                # assume the retrieved iterator is coming from sampler.
-                is_legacy = True
-
-            # validate the base generator name matches a sampler name.
-            if is_legacy or any(sampler_name == generator_name for sampler_name in samplers_names):
-
-                # wrap the generator into a `FastForwardSampler`
-                sampler = FastForwardSampler(generator, attr_name=generator_attr_name)
+            # wrap the generator into a `FastForwardSampler`
+            sampler = FastForwardSampler(generator, attr_name=generator_attr_name)
 
-                # if `CaptureIterableDataset` was available, the sampler should reload its own state.
-                if self._state_dict is not None:
-                    sampler.load_state_dict(self._state_dict[generator_attr_name])
-                # store the samplers
-                self.samplers[generator_attr_name] = sampler
+            # if `CaptureIterableDataset` was available, the sampler should reload its own state.
+            if self._state_dict is not None:
+                sampler.load_state_dict(self._state_dict[generator_attr_name])
+            # store the samplers
+            self.samplers[generator_attr_name] = sampler
 
-                # replace generator with the generator from the `FastForwardSampler`.
-                dataset_dict[generator_attr_name] = iter(sampler)
+            # replace generator with the generator from the `FastForwardSampler`.
+            dataset_dict[generator_attr_name] = iter(sampler)
 
         self.reset_on_epoch()
 
diff --git a/pytorch_lightning/utilities/cloud_io.py b/pytorch_lightning/utilities/cloud_io.py
index 9b40f6d69cfad..2c9eb1f768d3c 100644
--- a/pytorch_lightning/utilities/cloud_io.py
+++ b/pytorch_lightning/utilities/cloud_io.py
@@ -19,7 +19,6 @@
 import fsspec
 import torch
 from fsspec.implementations.local import AbstractFileSystem, LocalFileSystem
-from packaging.version import Version
 
 
 def load(
@@ -59,12 +58,6 @@ def atomic_save(checkpoint: Dict[str, Any], filepath: Union[str, Path]) -> None:
     """
 
     bytesbuffer = io.BytesIO()
-    # Can't use the new zipfile serialization for 1.6.0 because there's a bug in
-    # torch.hub.load_state_dict_from_url() that prevents it from loading the new files.
-    # More details can be found here: https://github.com/pytorch/pytorch/issues/42239
-    if Version(torch.__version__).release[:3] == (1, 6, 0):
-        torch.save(checkpoint, bytesbuffer, _use_new_zipfile_serialization=False)
-    else:
-        torch.save(checkpoint, bytesbuffer)
+    torch.save(checkpoint, bytesbuffer)
     with fsspec.open(filepath, "wb") as f:
         f.write(bytesbuffer.getvalue())
diff --git a/pytorch_lightning/utilities/imports.py b/pytorch_lightning/utilities/imports.py
index edf5f75aee6a9..5db24fe0f5cff 100644
--- a/pytorch_lightning/utilities/imports.py
+++ b/pytorch_lightning/utilities/imports.py
@@ -70,7 +70,6 @@ def _compare_version(package: str, op: Callable, version: str, use_base_version:
 
 _IS_WINDOWS = platform.system() == "Windows"
 _IS_INTERACTIVE = hasattr(sys, "ps1")  # https://stackoverflow.com/a/64523765
-_TORCH_GREATER_EQUAL_1_7 = _compare_version("torch", operator.ge, "1.7.0")
 _TORCH_GREATER_EQUAL_1_8 = _compare_version("torch", operator.ge, "1.8.0")
 _TORCH_GREATER_EQUAL_1_8_1 = _compare_version("torch", operator.ge, "1.8.1")
 _TORCH_GREATER_EQUAL_1_9 = _compare_version("torch", operator.ge, "1.9.0")
@@ -112,4 +111,4 @@ def _compare_version(package: str, op: Callable, version: str, use_base_version:
 
 # experimental feature within PyTorch Lightning.
 def _fault_tolerant_training() -> bool:
-    return _TORCH_GREATER_EQUAL_1_7 and int(os.getenv("PL_FAULT_TOLERANT_TRAINING", 0))
+    return bool(int(os.getenv("PL_FAULT_TOLERANT_TRAINING", 0)))
diff --git a/pytorch_lightning/utilities/seed.py b/pytorch_lightning/utilities/seed.py
index 3b20c53353411..e8fc243f484f8 100644
--- a/pytorch_lightning/utilities/seed.py
+++ b/pytorch_lightning/utilities/seed.py
@@ -21,7 +21,7 @@
 import numpy as np
 import torch
 
-from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_7, rank_zero_warn
+from pytorch_lightning.utilities import rank_zero_warn
 from pytorch_lightning.utilities.distributed import rank_zero_only
 
 log = logging.getLogger(__name__)
@@ -113,9 +113,7 @@ def pl_worker_init_function(worker_id: int, rank: Optional[int] = None) -> None:
     np.random.seed(ss.generate_state(4))
     # Spawn distinct SeedSequences for the PyTorch PRNG and the stdlib random module
     torch_ss, stdlib_ss = ss.spawn(2)
-    # PyTorch 1.7 and above takes a 64-bit seed
-    dtype = np.uint64 if _TORCH_GREATER_EQUAL_1_7 else np.uint32
-    torch.manual_seed(torch_ss.generate_state(1, dtype=dtype)[0])
+    torch.manual_seed(torch_ss.generate_state(1, dtype=np.uint64)[0])
     # use 128 bits expressed as an integer
     stdlib_seed = (stdlib_ss.generate_state(2, dtype=np.uint64).astype(object) * [1 << 64, 1]).sum()
     random.seed(stdlib_seed)
diff --git a/tests/callbacks/test_quantization.py b/tests/callbacks/test_quantization.py
index fa2ee767bdc8c..e3dfb9b6a7edf 100644
--- a/tests/callbacks/test_quantization.py
+++ b/tests/callbacks/test_quantization.py
@@ -31,7 +31,7 @@
 if _TORCH_GREATER_EQUAL_1_8:
     from torch.quantization import FakeQuantizeBase
 else:
-    # For torch 1.6 and 1.7.
+    # For torch 1.7.
     from torch.quantization import FakeQuantize as FakeQuantizeBase
 
 
diff --git a/tests/conftest.py b/tests/conftest.py
index 860f9357e4636..3d5548b7bd0ae 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -22,7 +22,7 @@
 import torch.distributed
 
 from pytorch_lightning.plugins.environments.lightning_environment import find_free_network_port
-from pytorch_lightning.utilities.imports import _TORCH_GREATER_EQUAL_1_7, _TORCH_GREATER_EQUAL_1_8
+from pytorch_lightning.utilities.imports import _TORCH_GREATER_EQUAL_1_8
 from tests import _PATH_DATASETS
 
 
@@ -95,10 +95,8 @@ def reset_deterministic_algorithm():
     yield
     if _TORCH_GREATER_EQUAL_1_8:
         torch.use_deterministic_algorithms(False)
-    elif _TORCH_GREATER_EQUAL_1_7:
+    else:
         torch.set_deterministic(False)
-    else:  # the minimum version Lightning supports is PyTorch 1.6
-        torch._set_deterministic(False)
 
 
 @pytest.fixture
diff --git a/tests/core/test_metric_result_integration.py b/tests/core/test_metric_result_integration.py
index 12fe7f2fb4652..9ec2f150ac5d4 100644
--- a/tests/core/test_metric_result_integration.py
+++ b/tests/core/test_metric_result_integration.py
@@ -33,7 +33,7 @@
     ResultCollection,
     ResultMetric,
 )
-from pytorch_lightning.utilities.imports import _fault_tolerant_training, _TORCH_GREATER_EQUAL_1_7
+from pytorch_lightning.utilities.imports import _fault_tolerant_training
 from tests.helpers import BoringModel
 from tests.helpers.runif import RunIf
 
@@ -470,21 +470,18 @@ def on_epoch_end(self) -> None:
 
 
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="Requires at least PyTorch 1.7")
 def test_result_collection_reload(tmpdir):
     result_collection_reload(default_root_dir=tmpdir)
 
 
 @RunIf(min_gpus=1)
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="Requires at least PyTorch 1.7")
 def test_result_collection_reload_1_gpu_ddp(tmpdir):
     result_collection_reload(default_root_dir=tmpdir, strategy="ddp", gpus=1)
 
 
 @RunIf(min_gpus=2, special=True)
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="Requires at least PyTorch 1.7")
 def test_result_collection_reload_2_gpus(tmpdir):
     result_collection_reload(default_root_dir=tmpdir, strategy="ddp", gpus=2)
 
diff --git a/tests/helpers/datamodules.py b/tests/helpers/datamodules.py
index 0cb178a749a09..78e806b37937e 100644
--- a/tests/helpers/datamodules.py
+++ b/tests/helpers/datamodules.py
@@ -46,7 +46,6 @@ def prepare_data(self):
         self.dataset_cls(self.data_dir, train=False, download=True)
 
     def setup(self, stage: Optional[str] = None):
-        # TODO: need to split using random_split once updated to torch >= 1.6
         if stage == "fit" or stage is None:
             self.mnist_train = self.dataset_cls(self.data_dir, train=True)
         if stage == "test" or stage is None:
diff --git a/tests/loops/optimization/test_optimizer_loop.py b/tests/loops/optimization/test_optimizer_loop.py
index 7e17cbbd56645..ae77c4387a398 100644
--- a/tests/loops/optimization/test_optimizer_loop.py
+++ b/tests/loops/optimization/test_optimizer_loop.py
@@ -24,7 +24,6 @@
 from pytorch_lightning.loops.optimization.optimizer_loop import ClosureResult
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from tests.helpers import BoringModel
-from tests.helpers.runif import RunIf
 
 
 def test_closure_result_deepcopy():
@@ -140,7 +139,6 @@ class CustomException(Exception):
     pass
 
 
-@RunIf(min_torch="1.7.0")
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
 @pytest.mark.parametrize("stop_epoch", (0, 1))
 @pytest.mark.parametrize("stop_batch", (0, 1, 2))
diff --git a/tests/loops/test_loops.py b/tests/loops/test_loops.py
index bad9a717d1629..8166f14754a51 100644
--- a/tests/loops/test_loops.py
+++ b/tests/loops/test_loops.py
@@ -253,7 +253,6 @@ def on_load_checkpoint(self, state_dict: Dict) -> None:
     assert state_dict == {"state_dict": {"a": 1}, "progress": {"increment": 1}}
 
 
-@RunIf(min_torch="1.7.0")
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
 @pytest.mark.parametrize("stop_epoch", (1, 2))
 @pytest.mark.parametrize("stop_batch", (1, 2))
@@ -323,7 +322,6 @@ def val_dataloader(self):
     assert trainer.fit_loop.epoch_loop.val_loop.epoch_loop.batch_progress.state_dict() == expected
 
 
-@RunIf(min_torch="1.7.0")
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
 @pytest.mark.parametrize("accumulate_grad_batches", (1, 2, 3))
 @pytest.mark.parametrize("n_optimizers", (1, 3, 5))
@@ -526,7 +524,6 @@ def configure_optimizers_multiple(self):
     assert state_dict["epoch_progress"]["current"]["started"] == stop_epoch
 
 
-@RunIf(min_torch="1.7.0")
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
 @pytest.mark.parametrize("n_optimizers", (1, 3, 5))
 def test_loop_state_on_complete_run(n_optimizers, tmpdir):
@@ -662,7 +659,6 @@ def train_dataloader(self):
     assert checkpoint["loops"]["fit_loop"] == expected
 
 
-@RunIf(min_torch="1.7.0")
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
 def test_fit_loop_reset(tmpdir):
     """Test that the reset logic in fit- and epoch loop is aware of whether the loop is restarting from a completed
@@ -752,7 +748,6 @@ def test_fit_loop_reset(tmpdir):
 
 
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0")
 @pytest.mark.parametrize(
     ["train_datasets", "val_datasets"],
     [([RandomDataset], [RandomDataset]), ([RandomDataset], [RandomDataset, RandomDataset])],
diff --git a/tests/plugins/test_double_plugin.py b/tests/plugins/test_double_plugin.py
index cadd02c692af5..b3fdf87428522 100644
--- a/tests/plugins/test_double_plugin.py
+++ b/tests/plugins/test_double_plugin.py
@@ -20,7 +20,6 @@
 
 from pytorch_lightning import Trainer
 from pytorch_lightning.plugins import DoublePrecisionPlugin
-from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_7
 from tests.helpers.boring_model import BoringModel, RandomDataset
 from tests.helpers.runif import RunIf
 
@@ -137,10 +136,7 @@ def on_fit_start(self):
     [
         DoublePrecisionBoringModel,
         DoublePrecisionBoringModelNoForward,
-        pytest.param(
-            DoublePrecisionBoringModelComplexBuffer,
-            marks=pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="torch.complex not available"),
-        ),
+        DoublePrecisionBoringModelComplexBuffer,
     ],
 )
 def test_double_precision(tmpdir, boring_model):
diff --git a/tests/profiler/test_profiler.py b/tests/profiler/test_profiler.py
index c4bcb56ca87bb..37756fcc62351 100644
--- a/tests/profiler/test_profiler.py
+++ b/tests/profiler/test_profiler.py
@@ -26,7 +26,6 @@
 from pytorch_lightning.loggers.tensorboard import TensorBoardLogger
 from pytorch_lightning.profiler import AdvancedProfiler, PassThroughProfiler, PyTorchProfiler, SimpleProfiler
 from pytorch_lightning.profiler.pytorch import RegisterRecordFunction
-from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_7
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from pytorch_lightning.utilities.imports import _KINETO_AVAILABLE
 from tests.helpers import BoringModel, ManualOptimBoringModel
@@ -394,8 +393,7 @@ def test_pytorch_profiler_nested(tmpdir):
 
     names = {"a", "b", "c"}
     ops = {"add", "empty", "fill_", "ones", "zero_", "zeros"}
-    if _TORCH_GREATER_EQUAL_1_7:
-        ops = {"aten::" + op for op in ops}
+    ops = {"aten::" + op for op in ops}
 
     expected = names.union(ops)
     assert events_name == expected, (events_name, torch.__version__, platform.system())
diff --git a/tests/trainer/connectors/test_checkpoint_connector.py b/tests/trainer/connectors/test_checkpoint_connector.py
index 6b408845ed879..4a42265eb21b0 100644
--- a/tests/trainer/connectors/test_checkpoint_connector.py
+++ b/tests/trainer/connectors/test_checkpoint_connector.py
@@ -21,7 +21,6 @@
 from pytorch_lightning.callbacks import ModelCheckpoint
 from pytorch_lightning.trainer.states import TrainerFn
 from tests.helpers import BoringModel
-from tests.helpers.runif import RunIf
 
 
 class HPCHookdedModel(BoringModel):
@@ -133,7 +132,6 @@ def test_hpc_max_ckpt_version(tmpdir):
 
 
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0")
 def test_loops_restore(tmpdir):
     """Test that required loop state_dict is loaded correctly by checkpoint connector."""
     model = BoringModel()
diff --git a/tests/trainer/connectors/test_signal_connector.py b/tests/trainer/connectors/test_signal_connector.py
index 3da8c100fe40c..aa5407e2f1228 100644
--- a/tests/trainer/connectors/test_signal_connector.py
+++ b/tests/trainer/connectors/test_signal_connector.py
@@ -26,7 +26,7 @@
 
 @pytest.mark.parametrize("register_handler", [False, True])
 @pytest.mark.parametrize("terminate_gracefully", [False, True])
-@RunIf(min_torch="1.7.0", skip_windows=True)
+@RunIf(skip_windows=True)
 def test_fault_tolerant_sig_handler(register_handler, terminate_gracefully, tmpdir):
 
     # hack to reset the signal
diff --git a/tests/trainer/test_data_loading.py b/tests/trainer/test_data_loading.py
index 0f6abd38e6836..97097b2074ca1 100644
--- a/tests/trainer/test_data_loading.py
+++ b/tests/trainer/test_data_loading.py
@@ -26,7 +26,7 @@
 from tests.helpers.runif import RunIf
 
 
-@RunIf(skip_windows=True, min_torch="1.7.0")
+@RunIf(skip_windows=True)
 @pytest.mark.parametrize("mode", (1, 2, 3))
 def test_replace_distributed_sampler(tmpdir, mode):
     class IndexedRandomDataset(RandomDataset):
diff --git a/tests/trainer/test_supporters.py b/tests/trainer/test_supporters.py
index e4598550c24fb..694d473155439 100644
--- a/tests/trainer/test_supporters.py
+++ b/tests/trainer/test_supporters.py
@@ -35,7 +35,6 @@
 from pytorch_lightning.utilities.auto_restart import CaptureMapDataset, FastForwardSampler
 from pytorch_lightning.utilities.data import get_len
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
-from pytorch_lightning.utilities.imports import _TORCH_GREATER_EQUAL_1_7
 from tests.helpers.boring_model import RandomDataset
 
 
@@ -312,7 +311,6 @@ def test_nested_calc_num_data(input_data, compute_func, expected_length):
     assert calculated_length == expected_length
 
 
-@pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="Requires at least PyTorch 1.7")
 @mock.patch.dict(os.environ, {"CUDA_VISIBLE_DEVICES": "0,1", "PL_TRAINER_GPUS": "2"})
 @mock.patch("torch.cuda.device_count", return_value=2)
 @mock.patch("torch.cuda.is_available", return_value=True)
diff --git a/tests/utilities/test_auto_restart.py b/tests/utilities/test_auto_restart.py
index 4e3385cebecbc..b36a9d1d76941 100644
--- a/tests/utilities/test_auto_restart.py
+++ b/tests/utilities/test_auto_restart.py
@@ -690,7 +690,6 @@ def create_dataloader():
     }
 
 
-@RunIf(min_torch="1.7.0")
 @pytest.mark.parametrize("use_fault_tolerant", ["0", "1"])
 def test_data_loading_wraps_dataset_and_samplers(use_fault_tolerant, tmpdir):
     """This test ensures the dataset and sampler are properly wrapped when fault tolerant is enabled."""
@@ -785,7 +784,6 @@ def __len__(self):
 
 # TODO: test with `RandomGeneratorGetItemDataset`
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0")
 @pytest.mark.parametrize(
     "dataset_class",
     [
@@ -921,7 +919,6 @@ def _run_training(trainer_kwargs, dataset_classes, fail_on_step: int = -1, ckpt_
 
 
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0")
 @pytest.mark.parametrize(
     "dataset_classes",
     [
@@ -975,7 +972,6 @@ def test_dataset_rng_states_restart_with_lightning(tmpdir, dataset_classes, mult
 
 
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0")
 @pytest.mark.parametrize(
     ["train_datasets", "val_datasets"],
     [
@@ -1139,7 +1135,7 @@ def _fit_model(
 @pytest.mark.parametrize("failure_on_training", [False, True])
 @pytest.mark.parametrize("failure_on_step", [False, True])
 @mock.patch.dict(os.environ, {"PL_FAULT_TOLERANT_TRAINING": "1"})
-@RunIf(min_torch="1.7.0", skip_windows=True)
+@RunIf(skip_windows=True)
 def test_auto_restart_under_signal(on_last_batch, val_check_interval, failure_on_training, failure_on_step, tmpdir):
     """This test asserts that if a signal is being sent during the training / validation phase, the model should
     restart in a reproducible way."""