He is a well-known interpreter of contemporary classical music and living composers, including Hans Werner Henze, William Bolcom, Lou Harrison, Alan Hovhaness, John Cage, Philip Glass, Giya Kancheli, Arvo Pärt,Virgil Thomson and Aaron Copland. He commissioned new compositions and has led the first performances and included many pieces of living composers, as well as the standard classical repertoire. Worth noting are the recordings of Copland's Appalachian Spring with the Saint Paul Chamber Orchestra in 1979, for which he won a Grammy Award ; Arvo Pärt's Fratres and Miserere; and many of the symphonies of opera's and Philip Glass, including his Fifth Symphony is dedicated to Davies. Lou Harrison's 3rd Symphony is also dedicated to Davies.
Davies was Music Director of the Saint Paul Chamber Orchestra in the years 1972-1980. Together with the composer Francis Thorne he founded the American Composers Orchestra in New York in 1977. He led that Orchestra until 2002. Davies was Music Director of the Brooklyn Philharmonic from 1990 to 1996.
In 1980 he went to Stuttgart in Germany, where he was the General Music Director of the Württembergischen Staatstheater (1980-1987). He spent there two operas by Philip Glass premiered, and performed a lot of operas from from the standard repertoire with often innovative and unusual stagings. He has worked with many directors, including Robert Altman in a cooperation for Salomé in Hamburg. Davies was also principal conductor of the Stuttgart Chamber Orchestra, the Orchestra of the Beethovenhalle in Bonn (1987-1995) and the Vienna Radio Symphony Orchestra. He is currently Chief conductor of the Bruckner Orchestra Linzand the Linz Opera since 2002, with a contract until 2014. 
Davies led several festival orchestras, including the Aspen Music Festival, the Cabrillo Music Festival, the Saratoga Music Festival, and the Bayreuthfestival, where he led a production of the opera Der fliegende Holländer, as the second American conductor ever, and also as one of youngest (1978-1980). Davies is Professor of conducting at the Mozarteum in Salzburg.
In March 2008, Davies was named the new music director of the Basel Symphony Orchestra, starting from the 2009-2010 season, with an initial contract of 5 years.