AbstractShape-memory polymers (SMPs) are stimuli-responsive materials, which allow spatially directed movements of devices upon external stimulation. This programmed movement is highly defined as it relies on the recovery of a device from a temporary, second shape to a permanent shape. The types of applicable stimuli to induce the shape switching as well as the specific conditions of material response can be tuned by altering the chemistry as well as the material organization on different hierarchical levels. Their ability to rapidly and automatically respond to changes in the environment makes SMPs suitable for a variety of biomedical applications, particularly for devices for minimally invasive surgery and for the delivery of therapeutics and cells. This article introduces the concepts of the shape-memory effect in polymers and their contribution to upcoming clinical demands for smart medical devices.