His paternal grandfather was a Mexican folk musician in the northern states of Sonora and Chihuahua.

Márquez studied composition from 1976 to 1979 with Federico Ibarra, Joaquín Gutiérrez Heras, and Héctor Quintanar.

[2] Until the 1990s, Márquez music was largely unknown outside his native country, which changed when he was introduced to the world of Latin ballroom dancing, which led to his most famous compositions the Danzones.

2 was included on the program of the Simon Bolívar Youth Orchestra conducted by Gustavo Dudamel on the 2007 tour of Europe and the United States.

[4] The composition has also opened the door for the discovery of other pieces by the composer that are increasingly being performed throughout the world and extensively in Latin America.

He was awarded the National Prize for Arts and Sciences (Mexico) by President Felipe Calderón on December 14, 2009.

In 2005, the Arturo Márquez International Music Festival was commenced in Caracas, Venezuela in honor of the composer.