Rafael Alvarez was born in Mexico City in 1970. He gained his musical education initially at the National Concservatoire in Mexico (Conservatorio Nacional de Música, 1987–1995), studying singing with Antonio López and choral conducting with Yorda Ramiro. In 1995–1996 he was awarded a scholarship to study at the Vienna Musikhochschule. For three years he performed at the Mexican National Opera (Opera Nacional de México), where he undertook the following roles, among others: Nemorino (L'elisir d'amore), Duke of Mantua (Rigoletto), Ferrando (Così fan tutte) and Almaviva (Il barbiere di Siviglia).
He also guest appeared at the Teatro Trujillo in Peru (Alfredo in La traviata and Edgardo in Lucia di Lammermour). In November 1997 he won the Prize for the best interpretation in the Carlo Morelli Singing Competition in Mexico City. He then left for Vienna, where he performed at the Neue Oper Wien. In the years that followed he took part in masterclasses with Ramón Vargas and Renata Scotto, as well as a German Lieder interpretation course with Leger Vandersteen at the Mexican Opera Studio S.I.V.A.M., and a lieder and oratorio course in Linz with P. Thomas Kerbl and AltheiBridges.
In 2006 he sang the role of Michel in Bohuslav Martinů's opera Juliette and Ferrando in Mozart's Così fan tutte, at the Schlosstheater in Schönbrunn. Since 2007 he has also been making regular appearances in a number of theatres in the Czech Republic (Plzeň, Ústí nad Labem, Liberec, Olomouc, Brno). He has also made guest appearances in Plovdiv in Bulgaria. In 2008 he made his debut at the Edinburgh Grand Opera as Faust. In 2009 he begun to cooperate regularly with the Prague State Opera (the Prince in Dvořák’s Rusalka, Duke of Mantua in Rigoletto, Pinkerton in Madama Butterfly, and others). In summer 2010, together with the Prague State Opera ensemble, he performed on tour at the Seoul Arts Centre (Don José in Carmen under the baton of Jiří Mikula).
In the 2010/2011 season he debuted at the Slovak National Theatre in Bratislava where he created Jacopo Foscari in the new production of Verdi’s I due Foscari under the baton of Friedrich Haider. Since 2012/2013 season he has been soloist of the National Theatre Brno.