Davies has led the Bruckner Orchestra Liza since 2002. He is the co-founder of the American Composers Orchestra, and served as the group's music director from 1975 to 2002; he remains its conductor laureate. He also held leadership positions with the Vienna Radio Symphony Orchestra, Brooklyn Philharmonic, Saint Paul Chamber Orchestra, and other groups; he directed the Cabrillo Music Festival, a center for new music, for 17 years.
A friend and champion of such composers as Philip Glass, John Cage, Lou Harrison, and William Bolcom, Davies has led the premieres of many works. Last month, he and the Bruckner Orchestra visited New York to give the world premiere of Glass's Eighth Symphony at the Brooklyn Academy of Music.