All of the wheels for 3.10 are missing. The 2 wheels that look like they are for 3.10 are for a RC release of Python 3.10 not final. Note the date on them is August 15, 2021 which is 2 months before 3.10 was complete. The wheels should be out in the next month. See #20039.

No, the 3.10 rc was explicitly ABI frozen so that it is compatible with the final release. The wheels published against it are intended to work with the final 3.10 release: #19630. macOS wheels were just too painful to build at the time (and I assume still are, which is why it's waiting for the next NumPy release.)

Any idea when this is going to be resolved? Appreciate all the hard work that goes into making this happen. :)

When azure-pipelines gets a 3.10 python in its image. This usually takes a few weeks from when the version is released.

Due this week for macOS and Windows, next week for Ubuntu:

actions/runner-images#4226 (comment)

Note that we only need the images for macOS and windows, manylinux provides it via the docker image.

Update (6:13 PM UTC): The images for 64 bit Python 3.10 are available on macOS and Windows. 32 bit Python 3.10 is missing from Windows, Python.h (3.10) is missing from macOS. Will check again later.

EDIT: requires latest Multibuild to even get started on macOS. @matthew-brett Does Multibuild have anything to do with the missing Python.h?

There are universal (fat) and arm64 wheels for NumPy 1.21.3 at https://pypi.org/project/numpy/#files. Do those fail to work for you? Progress on the x86_64 ones is waiting for multi-build/multibuild#438.