He has given numerous concerts all over the world, at international early music festivals such as those in Bruges, Utrecht, Caen, Saintes, Barcelona, Los Siglos de Oro of Caja Madrid and the Festival Internacional de Música y Danza in Granada as well as in concert halls that include the Auditórium Nacional de España, National Library of Washington, Opéra Comique of Paris, Teatro Real of Madrid, the Vienna Konzerthaus and many others.

Among his recordings there's a number of albums featuring Rivera as a soloist on the vihuela, theorbo and baroque guitar, as accompanist for the singers Marta Almajano and Carlos Mena, as the continuo player for the Al Ayre Español and as a member of Poema Harmonico.

He is the conductor for the ensemble La Correnta (which concentrates on Spanish Renaissance and Baroque repertoire) and Armoniosi Concerti.

He holds the professorship in plucked early instruments in the Conservatorio Superior de Música of Seville.