Eloy Barragán was born in México City and trained with the Escuela Nacional de Danza in México, Royal Academy of Dance in London, Boston Ballet and the Joffrey Ballet in New York . His professional career began with Joffrey II and the Washington Ballet before he became a soloist forCompañía Nacional de Danza in Mexico City . His career led him to Europe where he was a soloist for the Ballet Royal de Wallonie, Mainz Stattheater, and Dortmundt Stattheater. He then returned to Mexico to perform as a soloist for Ballet de Monterrey. Upon returning to the United States, he danced for Rebecca Kelly Dance Co. and New York Theater Ballet before he finally became a principal dancer, regisseur, and Ballet Master from 1996 through 2002 for the Eugene Ballet and Ballet Idaho. Throughout his career as a dancer, Eloy worked closely with numerous master choreographers, notably Vincente Nevrada, Youry Vamos, Anne Marie De Angelo, Jorge Lefebre, and Choo-San Goh. These influences led Eloy to a choreographic career of his own. Eloy has created new works for Ballet Idaho and Eugene Ballet; Caras, Danza Danzon, Blues Man, and Encuentros, Utah Ballet; Between Signs and Vuelo Conmigo. Eloy's most recent work includes pieces for the Richmond Ballet (Y Por Ti...), Beijing Dance Academy, (Primer Paso), and Endure for a collaborative performance with the Maia Quartet.

Eloy was awarded the 2000 Lifetime Career Fellowship by the Idaho Commission of the Arts. He has also received a choreographer's fellowship from the National Endowment for the Arts and the Boise Arts Council to create new work for the Eugene Ballet Company and Ballet Idaho .

His contemporary ballet choreography has been presented internationally at such venues as the Bolshoi Theatre, Finnish National Opera House, Conservatoire de Paris – Cité de la Musique, Alex Theater, Irvine Barclay Theater, New York City Center, and the National Ballet of Panamá presented two entire evenings of his work at El Teatro Nacional de la Republica de Panamá.

Currently, Eloy is an Associate Professor of Ballet and Choreography at the University of Iowa. Eloy Barragán is an ABT® Certified Teacher, who has successfully completed the ABT® Teacher Training Intensive in Primary through Level 7 and Partnering of the ABT® National Training Curriculum.