In 1960, he attended Alejandro Garcia Caturla Conservatory of Music, where he learned saxophone and clarinet In 1965, he was a featured soloist with the Cuban National Symphony Orchestra.

In an interview with ReasonTV, D'Rivera recalled that the Cuban communist government described jazz and rock and roll as "imperialist" music that was officially discouraged in the 1960s/70s, and that a meeting with Che Guevara sparked his desire to leave Cuba.

[4] In early 1980, while on tour in Spain, he sought asylum with the American Embassy, leaving his wife and child and Brother Enrique Who is also a saxophonist behind, with a promise to bring them out of Cuba.

[10] The band backing D'Rivera consists of Peruvian bassist Oscar Stagnaro, Argentinean trumpeter Diego Urcola, American drummer Mark Walker, and pianist Alex Brown.

[14] With Diego Urcola Quartet With David Amram With Mario Bauza With Caribbean Jazz Project With Gloria Estefan With Carlos Franzetti With Dizzy Gillespie With Conrad Herwig With Irakere With Yo-Yo Ma With Andy Narell With Daniel Ponce With Claudio Roditi With Lalo Schifrin With Bebo Valdés With others