He has performed in numerous concert halls and appeared at a wide variety of festivals, including the Teatro La Fenice, the Arsenal Concert Hall (Metz), the Auditorio Nacional (Madrid), the San Sebastián Music Fortnight, the Royal Academy of Music, the St. Petersburg Hermitage, the Hamburger Ostertöne, the Palacio Euskalduna, the Stuttgart Staatsoper, the Granada Music and Dance Festival, the Venice Biennial, the Kursaal in San Sebastián, the Mostly Modern Series in Dublin and the St. Petersburg Philharmonia.

Iñaki Alberdi is a frequent guest performer with ensembles such as the Royal Liverpool Philharmonic, the Tampere Chamber, the National Spanish Orchestra, the City of Granada Orchestra, the Spanish Radio and Television Symphony Orchestra, the Galicia Philharmonic, the Orchestra of the Region of Madrid, the Bilbao Symphony Orchestra, the Andorra National Chamber Orchestra, the Magnitogorsk Symphony Orchestra, the Málaga Philharmonic Orchestra, the Euskadi Symphony Orchestra, and the Russian Ministry of Culture Orchestra. Among other conductors, he has performed under Juanjo Mena, Josep Pons, Pablo González, Vasily Petrenko, Adrian Leaper, Pedro Halffter, Alexei Artemiev, Yoav Talmi, Mélanie Thiébaut, Nacho de Paz and José Ramón Encinar.

As a chamber music performer, he has worked with BCN 216, Ostots, Proyecto Guerrero, Taima-Granada, the Trío Arbós, the Kammerensemble Neue Musik (Berlin), VOX 21, the Ensemble Instrumental (Granada), the Ensemble Residencias (at the Centre for the Dissemination of Contemporary Music), the KEA Vocal Group, and Neue Vocalsolisten.
In Sofia Gubaidulina’s words, Iñaki Alberdi has great talent, and the complete dedication of an artist to his music. His amazing understanding of the depth of form, together with his remarkable temperament, made the strongest and most extraordinary impression on me”.