In 1966, as a recipient of a full scholarship from the Organization of American States, Reyes went to the United States to study at the Indiana University School of Music with American pianist, Sidney Foster, the first Leventritt Award winner and a pupil of David Saperton at the Curtis Institute of Music.

[1] In 1971, as a laureate of the Leventritt Competition in the United States, Reyes made his first North American tour.

[1][3] Reyes is also a prize winner in the Van Cliburn (U.S.) and Rio de Janeiro (Brazil) international competitions, and has recorded Liszt's Complete Paraphrases and Transcriptions from Verdi Operas for Connoisseur Society.

Two of those transcriptions, Salve Maria from I Lombardi and Simon Boccanegra were the object of piracy in the notorious Joyce Hatto recording scandal.

His recording Alberto Reyes plays Bach-Busoni, Chopin, Franck, Schumann, released by VAI in December 2016, was named Editor's Choice by Gramophone in its July 2017 issue.