The Buran spacecraft flew only once, an unmanned robotic test flight on November 15, 1988.
The Soviet space program collapsed with the Soviet Union. and the Buran program was never resumed. The Buran orbiter (one hesitates to call it a "shuttle", since it never flew again) would have been carried piggyback aboard a transport aircraft, much as the American Space Shuttles are. However, the Buran orbiter was damaged in a hangar collapse in 2002 and is now incapable of flight.