The Aeronautics and Air Astronautics Museum, more commonly known as the Air Museum, has been on the Cuatro Vientos airbase since 1981. It covers 70,000 square metres distributed over 7 hangars and 7 outdoor platforms, and holds 150 aircraft (planes and helicopters) as well as uniforms, decorations, engines, models, weapons and other aviation paraphernalia.

It has some unique items such as the Villanova-Acedo, the oldest Spanish airplane; the "Jesús del Gran Poder", which crossed the South Atlantic in 1929; the German Heinkel He-111 E-1 bomber; Juan de la Cierva's C-19 Autogiro, which flew in 1932; and a huge collection of engines.