In 1999, Seiji Ozawa named Volkov the assistant conductor with the Boston Symphony Orchestra.
[4] He was named the Royal Philharmonic Society Young Musician of the Year in 2004, in recognition of his work with the BBC SSO.
[5] In January 2011, the Iceland Symphony Orchestra named Volkov as its chief conductor and music director.
[12][13][14] Volkov and his partner Maya Dunietz have a daughter, Nadia, born in August 2007 in Israel.
[15][16] In Tel Aviv, Volkov and the jazz musician Assif Tsahar have established the performing venue Levontine 7.