Dog fight is a common term used to describe close-range aerial combat between two or more military aircraft. The term originated during World War I, and probably derives from the preferred fighter tactic of positioning one's aircraft behind the enemy aircraft. From this position, a pilot could fire his guns on the enemy without having to lead the target, and the enemy aircraft could not effectively fire back. When two fighter aircraft circled each other trying to achieve this position, it resembles two dogs chasing each other's tails.
Sorties in which the objective was to engage enemy fighters--often resulting in dogfights--were coloquialy referred to in WWII as a "Rodeo" or "Freijagd".
With modern air-to-air missiles greatly extending the general engagement range of jet fighters, the dog fight has gone largely out of existence. However, the US Navy (TOPGUN) and Air Force (Red Flag) continue to teach postgraduate level classes in air combat maneuvering (dogfighting) engagements.