Dogfight
A aerial conflict where 2 to a unlimited amount of fighter planes are involved, the goal is to destroy the other fighter planes, usually to clear a way for bombers.

The first dogfights were in World War 1.

The History Channel use to have a series about dogfights, called "Dogfights", using computer design to remake dogfights, look it up on YouTube, great show.
The dogfighter Bud Anderson engaged in many dogfights in WW2 in his P-51 Mustang "The Crow", he was a triple ace with 16 confirmed kills.