Considered one of the all-time greatest amateurs,[2] he became three-time Olympic gold medalist, and the World Champion six times in a row,[3] all in the heavyweight division.

[4] Savón is particularly known for having rejected numerous multimillion-dollar offers to defect and leave Cuba permanently to fight Mike Tyson as a professional.

[7][8] The only boxers, who got away with knockout victories over Savón unavenged were Soviet Usman Arsaliyev and North Korean Li Dal-Chen, whom he met only once.

[10] This set off his career, in which he would win six World Championships; his victory at the 1997 tournament was the result of the disqualification of an opponent, future professional world champion Ruslan Chagaev (whom Savón had previously beaten), who beat Savón in the final, but was later stripped of the gold medal for having two professional fights prior to the championships.

[16] Savón won three Olympic gold medals, a feat shared with only two other boxers, László Papp and compatriot Teófilo Stevenson.

[19] In February of the following year with Fidel Castro also present, Savón had the song "You Love Us" dedicated to him by the Manic Street Preachers, who became the first western rock band to play in Cuba.