AbstractMedical devices such as implants, surgical instruments, extracorporal devices or wound covers, as well as controlled drug delivery systems (CDDS) require a specific combination of material properties and functions including, e.g., mechanical stability, biocompatibility, or biofunctionality. Polymeric biomaterials are of high relevance for such applications, as properties and functions can be tuned in a wide range by only small defined variations of their chemical or morphological structure. The rapid progress in surgical techniques, especially in minimally-invasive surgery, requires smart materials, which are capable of an active on-demand movement and which do not need to be removed in a second surgery. These challenges can be addressed by shape-memory polymers (SMPs) described in this chapter. SMPs are of high technological significance for biomedical applications as they enable on demand predefined changes in the shape of a device upon exposure to a suitable stimulus. Multifunctional materials are obtained when the shape-memory effect is combined with an additional function such as hydrolytic degradability, biofunctionality, and controlled drug release. Selected biomaterials with shape-memory capability are presented, including data on their biocompatibility. The potential of SMPs as a platform technology for biomedical applications is sketched by an overview on SMP-based medical devices being developed and the potential use of SMPs as matrix for CDDS.