Air guitars are imaginary instruments. They are conjured from the imagination to allow the listener to play along to a piece of music (generally guitar-based music: I have not seen air guitars used to accompany choral music).
Strictly speaking, air guitars are not a brand as such, because each one is loving crafted by its user. Nevertheless, all follow similar design principles. Materials used in the construction of the traditional air guitar have not changed in years, namely: 78% nitrogen, 21% oxygen, 0.04% carbon dioxide and a dash of rock and roll.
Variations are the water guitar, that you can play in the bath and the tennis racket guitar (a distant cousin of the hairbrush microphone).