It has no place in air-to-air combat other than trying to not get shot down. It is a dedicated ground attack, CAS platform. It has seen plenty of use in that role in Iraq and Afghanistan. I believe the Soviets in Tom Clancy's Red Storm Rising, and the Taliban both refer to it as the "Devil's Cross".
Probably one of my greatest memories from NTC is being on a hill, and having an A-10 crest the hill, inverted, and then roll over as it continues down the other side on its way to attack a column of OPFOR armor. F-16s and F-18s would just zip right by and be gone in a second. The A-10s would lazily swing back and forth as they worked their way down the valley.
That 'crest the hill inverted' trick is insane... They do it because following the contour of the hill while flying right sire up would result in too many negative g's. By flipping inverted, the g-force is now 'down' (relative to the pilot) and they can pull a lot harder (since the body is much better at dealing with g-foreces in that direction).
I don't think there has been really Air - Air combat in a very long time. (Vietnam?) - though using this on a A10 makes a lot of sense, tricking ground forces yo think you're banking in their direction when your not and tricking enemy aircraft of the same can give an advantage.