Most air-superiority fighters are equipped exclusively with front-mounted weapons, leading planes to jockey for the critical trailing position behind one's opponent to strike a killing blow. This reportedly was the origin of the term "dogfight," with large-scale conflicts involving numerous aircraft being referred to as "furballs."
During World War I, reconnaissance planes were used to survey enemy positions from overhead for intelligence purposes, and sometimes aircraft were equipped with weapons to bombard entrenched positions. To counter use of these tactics by the enemy, air-superiority planes were developed to down enemy craft. Weight and maneuverability concerns limited weapon payloads; eventually fighters were exclusively armed with fixed forward-facing guns.
Dogfights continued in this fashion until the Vietnam War, which came with the advent of guided missiles. This technology was thought to obviate the need for skill in fighter combat, but the unreliability of weapons of that era forced dogfights to continue in standard fashion. Although modern technology allows air combat to take place beyond visual range (BVR), short-range combat can still occur within visual range (WVR).
Arcade style games such as the Ace Combat series often simplify the process of dogfighting, though that's not to say it is always easy. The dogfights may last a matter of seconds but will may be difficult due to the sheer number encountered per flight. In more realistic games the process is made much more technical as the game attempts to mimic real life. The player will have to avoid stalls, manage a radar and execute far more advanced manoeuvres to stand a chance.