The system status for TestFlight is green:
https://developer.apple.com/system-status/
and mentions having fixed an issue yesterday. TestFlight is currently presenting a "We are currently experiencing processing issues. Build processing may be delayed." message however.
We have a build that has been processing for 4+ hours now. We fired off another one in case the first one was just stuck / lost -- but that too has now been processing for more than 2 hours.