Most polymers used in clinical applications today are materials that have been developed originally for application areas other than biomedicine. On the other side, different biomedical applications are demanding different combinations of material properties and functionalities. Compared to the intrinsic material properties, a functionality is not given by nature but result from the combination of the polymer architecture and a suitable process. Examples for functionalities that play a prominent role in the development of multifunctional polymers for medical applications are biofunctionality (e.g. cell or tissue specificity), degradability, or shape-memory functionality. In this sense, an important aim for developing multifunctional polymers is tailoring of biomaterials for specific biomedical applications. Here the traditional approach, which is designing a single new homo- or copolymer, reaches its limits. The strategy, that is applied here, is the development of polymer systems whose macroscopic properties can be tailored over a wide range by variation of molecular parameters. The Shape-memory capability of a material is its ability to trigger a predefined shape change by exposure to an external stimulus. A change in shape initiated by heat is called thermally-induced shape-memory effect. Thermally, light-, and magnetically induced shape-memory polymers will be presented, that were developed especially for minimally invasive surgery and other biomedical applications. Furthermore triple-shape polymers will be introduced, that have the capability to perform two subsequent shape changes. Thus enabling more complex movements of a polymeric material.