Kremer's first concert in the West was in Viennas Musikverein in the year 1970, where he played with Thomas Schippers and Vienna Symphoniker. He debuted in Germany at the festival Bachwoche Ansbach and in the Berlin Philharmonie in 1975 and in London under André Previn in 1976, followed by appearances at the Salzburg Festival in 1976 and in New York City and in Japan in 1977. In 1981, Kremer founded a chamber music festival in Lockenhaus, Austria, with a focus on new and unconventional programming, serving as artistic director for 30 years. In 1996 Kremer founded the Kremerata Balticachamber orchestra, composed of young players from the Baltic region. He was also among the artistic directors of the festival "Art Projekt 92" in Munich and is director of the MusiksommerGstaad festival (1996/97) and Basel ("les musiques") in Switzerland. In 2007-2008, he and Kremerata Baltica toured with the classical musical comedy duo Igudesman & Joo. He also made regular appearances at the Verbier Festival until the summer of 2011, when he withdrew, issuing a public complaint of excessive hype.