The thermally-induced shape-memory effect (SME) is the capability of a material to change its shape in a predefined way in response to heat. In shape-memory polymers (SMP) this shape change is the entropy-driven recovery of a mechanical deformation, which was obtained before by application of external stress and was temporarily fixed by formation of physical crosslinks. The high technological significance of SMP becomes apparent in many established products (e.g., packaging materials, assembling devices, textiles, and membranes) and the broad SMP development activities in the field of biomedical as well as aerospace applications (e.g., medical devices or morphing structures for aerospace vehicles). Inspired by the complex and diverse requirements of these applications fundamental research is aiming at multifunctional SMP, in which SME is combined with additional functions and is proceeding rapidly. In this review different concepts for the creation of multifunctionality are derived from the various polymer network architectures of thermally-induced SMP. Multimaterial systems, such as nanocomposites, are described as well as one-component polymer systems, in which independent functions are integrated. Future challenges will be to transfer the concept of multifunctionality to other emerging shape-memory technologies like light-sensitive SMP, reversible shape changing effects or triple-shape polymers.