Estévez received degrees from the École Normale de Musique de Paris (Advanced Composition, 1984), the Sorbonne University of Paris (Ph.D. in Sociology, 1985), the National Conservatory of Music, Quito, Ecuador (Classical Guitar and Music Theory, 1980), and the Central University of Ecuador (Architecture, 1978).
Attended analysis seminars at the Conservatoire National Supérieur de Musique de Paris; electro-acoustics and computer music at the Centre Européen pour la Recherche Musicale in Metz; and pursued graduate studies in musicology (ABD) at the Sorbonne University.
 

Before traveling to France to specialize in composition, Estévez taught classical guitar and form analysis at the National Conservatory in Quito (1972-80). Upon returning from France, he rejoined the faculty of the National Conservatory, founded the Department of Composition, Musical Research and Outreach, and taught composition, orchestration, musical analysis, and computer-assisted music (1985-94).

Founded the Ecuadorean Festival of Contemporary Music and the series Music of our Times and directed them from 1987 to 1994.

Following an invitation to the SoundCelebration II festival, hosted by the Louisville Orchestra, Kentucky, in 1992, he moved to the USA in 1994, serving as a visiting composer-in-residence at the University of Louisville (1994-1997), and as composer-in-residence at Spalding University (1997-2002).

From 1992, and through his stay in the USA, he continued developing his creative work, completing music commissions, and attending invitations to disseminate his music.

Between 2009 and 2017, he intermittently commuted between USA and Ecuador, serving as a consultant to the National Symphony Orchestra (2009 to 2010) and as an adviser to the Minister of Culture (2011 to 2013). In 2012, he was appointed head of the project for the creation of the National University of the Arts, approved by the National Assembly in 2013. Estévez also served as a consultant to the Ministry of Education of Ecuador for the improvement of artistic education (2014-2015).

Estévez moved from Louisville to Denver in 2017, while setting his primary residence back in Quito.

Currently (2018), he is working on incidental and chamber music projects, as well as advocating for the revamping of the Ecuadorian Festival of Contemporary Music.

Relevant commissions: Ensemble SurPlus, Germany; Gary Barnett, piano; Institute for New Music of Freiburg, Ensemble Aventure of Germany, Nieuw Ensemble of Amsterdam; IBM Ecuador.