Growing up in the Upper West Side of Manhattan, Gilbert attended the Ethical Culture Fieldston School in Riverdale, where he was a top student.

[7] Gilbert's long association with Santa Fe Opera dates back to 1993, when he served as the orchestra's assistant concertmaster.

Prior to that, both of Gilbert's parents played in the opera's orchestra, and his father served as concertmaster for a number of years.

[9][10] Gilbert built much of his reputation conducting contemporary and American music, and his New York Philharmonic appointment marked somewhat of a shift by the orchestra away from his more conservative predecessors Lorin Maazel, Kurt Masur, and Zubin Mehta.

[12] For his inaugural 2009/10 Philharmonic season, Gilbert introduced a number of new initiatives, including the presence of Composer-in-Residence Magnus Lindberg and Artist-in-Residence Thomas Hampson.

In February 2015, the orchestra announced the scheduled conclusion of Gilbert's tenure as music director at the end of the 2016–2017 season.

In January 2020, the Royal Swedish Opera announced the appointment of Gilbert as its next music director, effective in the spring of 2021.

[18] In 2002, Gilbert married Swedish cellist Kajsa William-Olsson, a member of the Royal Stockholm Philharmonic Orchestra.