After his college years, Robertson began to receive conducting offers in Europe and performed often in both symphonic and operatic repertoire.
His early career lectured under the rubric of the U.S. Information Agency in the Middle East and around the world on the subject of music.
He and the ONL toured the United States in 2003, with concerts in New York City, Seattle, Berkeley, and Los Angeles.
Robertson is generally regarded as having restored the SLSO's artistic prominence after the sudden resignation of the prior music director Hans Vonk, and the orchestra's labor dispute in the winter of 2005.
[14] However, in June 2017, the orchestra noted an update to Robertson's contract, with a newly scheduled conclusion of his music directorship at the close of the 2017-2018 season, in a reversion of the December 2016 situation.
[16] With the SLSO, Robertson has conducted several commercial recordings of music of John Adams (composer) for the Nonesuch label.
[29] In February 2018, the Juilliard School announced the appointment of Robertson as its next director of conducting studies, effective with the 2018-2019 academic year.
[32] In December 2022, the Utah Symphony announced the appointment of Robertson as its first-ever creative partner, effective with the 2023-2024 season, with a contract of 3 years.
[33] Robertson has recorded for the Sony Classical, Harmonia Mundi, Naive, EMI/Virgin Classics, Atlantic/Erato, Nuema, Ades Valois, Naxos and Nonesuch labels, featuring the music of such composers as Adams, Bartók, Boulez, Carter, Dusapin, Dvorák, Ginastera, Lalo, Manoury, Milhaud, Reich, Saint-Saëns, and Silvestrov.
Robertson received the 2006 Ditson Conductor's Award from Columbia University for his championing of American music.
[37] On May 15, 2010, Robertson received the degree Doctor of Music honoris causa from Westminster Choir College in Princeton, New Jersey.
[39] Along with Diana Doherty, Sydney Symphony Orchestra, Nigel Westlake and Synergy Vocals, Robertson was nominated for the 2019 ARIA Award for Best Classical Album for the album Nigel Westlake: Spirit of the Wild / Steve Reich: The Desert Music.
The album is a recording of Nigel Westlake’s Spirit of the Wild and of Steve Reich’s The Desert Music with the latter conducted by Robertson.