The famous boxing match known as "The Fight of the Century" took place in 1971 between Muhammad Ali and Joe Frazier. This historic bout was significant for both its athletic competition and its cultural impact. They were each undefeated at the time, which added to the stakes and drama surrounding the fight. Frazier won the match by unanimous decision, and this event is still remembered as one of the most iconic moments in boxing history, representing the fierce rivalry between the two legendary fighters.