Curet Alonso's mother was a seamstress and his father a Spanish language teacher and musician who played in the band of Simón Madera.

[1] He was two years old in 1928, when his parents divorced and together with his mother and sister moved to Barrio Obrero, located in the Santurce section of San Juan with his grandmother.

[2][3] After he graduated from Central High School in Santurce, he enrolled in the University of Puerto Rico where he studied journalism and sociology.

Some of the people who have interpreted his songs are: Joe Quijano, Iris Chacón, Wilkins, Cheo Feliciano, Celia Cruz, La Lupe, Willie Colón, Tito Rodríguez, Olga Guillot, Mon Rivera, Héctor Lavoe, Ray Barretto, Tony Croatto, Rubén Blades, Tito Puente, Ismael Miranda, Roberto Roena, Bobby Valentín, Marvin Santiago, Willie Rosario, Menudo, Chucho Avellanet, Andy Montañez, Rafael Cortijo, Tommy Olivencia, and Frankie Ruiz.

His song Las Caras Lindas (De Mi Gente Negra) (The Beautiful Faces (Of My Black People) recorded by Ismael Rivera, is considered by many in Puerto Rico as a classic.

In 2009, US Federal Court in San Juan released 695 songs originally licensed to Fania, but the rest of the catalog is still in ACEMLA's hands, and the legal battles continue.

Rubén Blades suspended some dates from his "farewell" tour (before becoming the Minister of Tourism for Panama) to attend Curet Alonso's funeral.