At 2½ million US sales, it stands as the biggest selling non-English language album in American record history.

The title Canciones de Mi Padre refers to a booklet that the University of Arizona published in 1946 for Ronstadt's deceased aunt, Luisa Espinel, who had been an international singer in the 1920s.

Also, Ronstadt has credited the late Mexican singer Lola Beltrán as an influence in her own singing style, and she recalls how a frequent guest to the Ronstadt home, Eduardo "Lalo" Guerrero, father of Chicano music, would often serenade her as child with these songs.

Although sometimes referred to as Ronstadt's first Spanish-language recordings, in fact she had recorded several times in the language before, including "Lo Siento mi Vida", a song she co-wrote with her father for her 1976 album, Hasten Down the Wind, and "Lago Azul," a Spanish translation of "Blue Bayou", that was released as a single following her hit English version from her 1977 album, Simple Dreams.

In 2021, it was announced that Canciones de Mi Padre had been inducted into the Grammy Hall of Fame.