diff --git a/torch/utils/cpp_extension.py b/torch/utils/cpp_extension.py
index b84ebe95d525..7837d8cbb570 100644
--- a/torch/utils/cpp_extension.py
+++ b/torch/utils/cpp_extension.py
@@ -828,6 +828,35 @@ def CUDAExtension(name, sources, *args, **kwargs):
                 cmdclass={
                     'build_ext': BuildExtension
                 })
+
+    Compute capabilities:
+
+    By default the extension will be compiled to run on all archs of the cards visible during the
+    building process of the extension, plus PTX. If down the road a new card is installed the
+    extension may need to be recompiled. If a visible card has a compute capability (CC) that's
+    newer than the newest version for which your nvcc can build fully-compiled binaries, Pytorch
+    will make nvcc fall back to building kernels with the newest version of PTX your nvcc does
+    support (see below for details on PTX).
+
+    You can override the default behavior using `TORCH_CUDA_ARCH_LIST` to explicitly specify which
+    CCs you want the extension to support:
+
+    TORCH_CUDA_ARCH_LIST="6.1 8.6" python build_my_extension.py
+    TORCH_CUDA_ARCH_LIST="5.2 6.0 6.1 7.0 7.5 8.0 8.6+PTX" python build_my_extension.py
+
+    The +PTX option causes extension kernel binaries to include PTX instructions for the specified
+    CC. PTX is an intermediate representation that allows kernels to runtime-compile for any CC >=
+    the specified CC (for example, 8.6+PTX generates PTX that can runtime-compile for any GPU with
+    CC >= 8.6). This improves your binary's forward compatibility. However, relying on older PTX to
+    provide forward compat by runtime-compiling for newer CCs can modestly reduce performance on
+    those newer CCs. If you know exact CC(s) of the GPUs you want to target, you're always better
+    off specifying them individually. For example, if you want your extension to run on 8.0 and 8.6,
+    "8.0+PTX" would work functionally because it includes PTX that can runtime-compile for 8.6, but
+    "8.0 8.6" would be better.
+
+    Note that while it's possible to include all supported archs, the more archs get included the
+    slower the building process will be, as it will build a separate kernel image for each arch.
+
     '''
     library_dirs = kwargs.get('library_dirs', [])
     library_dirs += library_paths(cuda=True)
@@ -1496,16 +1525,24 @@ def _get_cuda_arch_flags(cflags: Optional[List[str]] = None) -> List[str]:
 
     # If not given, determine what's best for the GPU / CUDA version that can be found
     if not _arch_list:
-        capability = torch.cuda.get_device_capability()
-        supported_sm = [int(arch.split('_')[1])
-                        for arch in torch.cuda.get_arch_list() if 'sm_' in arch]
-        max_supported_sm = max((sm // 10, sm % 10) for sm in supported_sm)
-        # Capability of the device may be higher than what's supported by the user's
-        # NVCC, causing compilation error. User's NVCC is expected to match the one
-        # used to build pytorch, so we use the maximum supported capability of pytorch
-        # to clamp the capability.
-        capability = min(max_supported_sm, capability)
-        arch_list = [f'{capability[0]}.{capability[1]}']
+        arch_list = []
+        # the assumption is that the extension should run on any of the currently visible cards,
+        # which could be of different types - therefore all archs for visible cards should be included
+        for i in range(torch.cuda.device_count()):
+            capability = torch.cuda.get_device_capability(i)
+            supported_sm = [int(arch.split('_')[1])
+                            for arch in torch.cuda.get_arch_list() if 'sm_' in arch]
+            max_supported_sm = max((sm // 10, sm % 10) for sm in supported_sm)
+            # Capability of the device may be higher than what's supported by the user's
+            # NVCC, causing compilation error. User's NVCC is expected to match the one
+            # used to build pytorch, so we use the maximum supported capability of pytorch
+            # to clamp the capability.
+            capability = min(max_supported_sm, capability)
+            arch = f'{capability[0]}.{capability[1]}'
+            if arch not in arch_list:
+                arch_list.append(arch)
+        arch_list = sorted(arch_list)
+        arch_list[-1] += '+PTX'
     else:
         # Deal with lists that are ' ' separated (only deal with ';' after)
         _arch_list = _arch_list.replace(' ', ';')