His early studies at the choir school of the Benedictine Abbey of Santa Cruz del Valle de los Caídos were continued at the Royal Conservatoire in Madrid. He is a contributor to the Répertoire International des Sources Musicales (RISM); he has published numerous articles on the Códice de Madrid and the Las Huelgas Codex, and he has published a monograph for Alianza Editorial entitled El Canto Gregoriano. Asensio continues to collaborate with the Atêlier de Paléographie Musicale at Solesmes and in Salamanca he served as Professor of Musicology at the Royal Conservatoire.

Asensio currently holds dual appointments as Professor of Musicology at both Barcelona’s Escola Superior de Músicade Catalunya and Madrid’s Royal Conservatoire. He has directed Schola Antiqua since 1996 and since 2001 he has been a member of the Consiglio Direttivo of AISCGre. In addition, he is a research associate with CILengua, a member of the study group Bibliopegia, editor of the scholarly journal Estudios Gregorianos and member of the Ecclesiastical Sciences Academy of San Dámaso.