Álvarez competed on tour in the 1990s and early 2000s, reaching a best singles ranking of 288 in the world. His only ATP Tour main draw appearances came at Bordeaux in 1992, where he lost in the first round to the eighth-seed Fabrice Santoro…
Between 1951 and 1955, Alvarez studied at the Escuela Nacional de Bellas Artes "San Alejandro" in Havana. In 1958, he studied drawing and painting in the École nationale supérieure des Beaux-Arts in Paris, France.