The FAA controls just about everything about civilian aircraft in US airspace in terms of regulation, certification, flight rules, etc. Do they have any authority over military aircraft beyond requiring military flights to communicate with ATC for safety and designating certain areas as military airspace?
This question addresses retired military aircraft in civilian use, and one of the answers to this question mentions a "Surplus military" category, but nothing about active military. I'm asking about current, active military aircraft in terms of certification, pilot licensing/qualification, etc.