The present invention pertains to copolymers having one or more polyisobutylene segments and one or more biodegradable polymer segments, to methods of making such copolymers, to medical articles that contain such copolymers, and to methods of making such medical articles. According to certain aspects of the invention, copolymers are provided, which comprise a plurality of polyisobutylene segments and a plurality of biodegradable polymer segments. According to certain aspects of the invention, copolymers are provided, which comprise urethane linkages, urea linkages, amide linkages, ester linkages, anhydride linkages, carbonate linkages, linkages commonly described as “click” chemistry linkages, and combinations of two or more types of such linkages.