The present invention is directed to polymeric compositions comprising a biodegradable copolymer that possesses shape-memory properties and implantable devices (e.g., drug-delivery stents) formed of materials (e.g., a coating) containing such compositions. The polymeric compositions can also contain at least one non-fouling moiety, at least additional biocompatible polymer, at least one biobeneficial material, at least one bioactive agent, or a combination thereof. The polymeric compositions are formulated to possess good mechanical, physical and biological properties. Moreover, implantable devices formed of materials comprising such compositions can be delivered to the treatment site in a conveniently compressed size and then can expand to dimensions appropriate for their medical functions.