FIR and sovereign ('national') air space
I'm no expert in this area at all but there a number of countries that claim, unilaterally, that their FIR equates to sovereign airspace. This is based on the proximate International law relating to Continental Shelves and the upwards projection thereof.
Accordingly, the two countries that I am referring to (and anyone in NATO can probably work out which two) frequently have armed stand-offs when military aircraft from their neighbours get airborne and nudge the FIR boundaries. It has led to accidents in the past, especially when the aircraft are supporting surface units exercising their right of innocent passage through particular straits. I foolishly mentioned in discussion with the locals that an FIR boundary wasn't a national boundary; the resultant discussion was rather unpleasant and eventually turned into an anti 'English' rant based on mid 19th century annotations on Admiralty Charts, which have been used to justify each other's national positions.
I walked away, shaking my head and murmuring 'Hmmm, that went well, then...'