One of the best books I have read on the subject (and the list is long
) is Robert Jackson's "Air War Over Korea. The analysis of the air strategies employed by both sides alone makes this book worth reading.
The real crux of this book though is the detail with which he addresses the build up of forces and the application of 'all' air operations. Most books are fixated on the battle between the MiG and the Sabre. Jackson provides a much more balanced overview; assessing the success (or otherwise) of the ground support roll played by the both sides, the strategic and tactical bombing efforts by the B-29 and A-26 crews, the impact and function of the USN, Marine and FAA as weel as the air superiority role of the Sabre.
One of the really interesting points highlighted is the diversity of missions flown by the MiG pilots. The point made is that as many missions flown were intercept in nature - against the Mustang, F-80, F-84, A-26 and B-29 - as opposed the the generally accepted fighter sweeps against the Sabre's.
There is an extensive list of UN OOB's and stastics covering aircraft claims, missions flown by all types, enemy material destroyed, carriers employed etc. He doesn't attempt to confirm or otherwise the claim of 792 MiG's claimed shot down. Irrespective of whether the claims are correct or not (and until sources in China and North Korea become available the question is moot), but the point made is that the UN air forces remained on the offensive for almost the whole war. And that, despite quite severe losses, the ground attack component was the telling force in what was in effect a UN air victory.
That victory though came at some cost. In all the UN (predominately USAF) air forces lost almost 3,200 aircraft, approximately just over a third to flak alone. For the USAF they lost the equivalent of 20 combat Groups - roughly one quarter of the USAF's total front line strength as it stood in June 1950!
The lasting effect of the Korean air war was that it woke the American politicians up from the stupor they had allowed the Armed Forces to plunge into after the success of WWII. A whole raft of new military and strategic policies were put into effect to ensure that America would not be found so ill-equipped again.