Polymeric materials are clinically required for medical devices, as well as controlled drug delivery systems. Depending on the application, the polymer has to provide suitable functionalities, for example, mechanical functions or the capability to actively move, so that an implant can be inserted in a compact shape through key-hole incisions and unfold to its functional shape in the body. Shape-memory polymers, as described herein regarding their general principle, compositions and architectures, have developed to a technology platform that allows the tailored design of such multifunctionality. In this way, defined movements of implants triggered either directly or indirectly, tailored mechanical properties, capability for sterilization, biodegradability, biocompatibility and controlled drug release can be realized. This comprehensive review of the scientific and patent literature illustrates that this technology enables the development of novel medical devices that will be clinically evaluated in the near future.