The present invention pertains to polyisobutylene urethane, urea and urethane/urea copolymers, to methods of making such copolymers and to medical devices that contain such polymers. According to certain aspects of the invention, polyisobutylene urethane, urea and urethane/urea copolymers are provided, which comprise a polyisobutylene segment, an additional polymeric segment that is not a polyisobutylene segment, and a segment comprising a residue of a diisocyanate. According to other aspects of the invention, polyisobutylene urethane, urea and urethane/urea copolymers are provided, which comprise a polyisobutylene segment and end groups that comprise alkyl-, alkenyl- or alkynyl-chain-containing end groups.