The ability of polymers to move actively in response to an external stimulus such as heat or light is of high scientific and technological significance. In any instance stimuli-responsive effects on the molecular level are converted into macroscopic movement, whereby generally two different moving behaviors have to be differentiated for polymer-based materials: the shape-memory effect and the shape-changing capability. Basic concepts for the molecular design of suitable polymer architectures for shape-memory polymers as well as tailored programming processes are presented. The thermally-induced shape-memory effect of polymers is described as well as the extension of this concept to other stimuli than heat. Indirect actuation of the thermally-induced effect by IR-irradiation, electric current, humidity or alternating magnetic fields are outlined as well as recent work on light-induced shape-memory polymers. For shape-changing polymers, two basic concepts are presented: shape changes occurring during phase orientation of liquid crystal elastomers (LCE) and the photomechanical effect based on photoisomerization of moieties, such as azo-groups incorporated in suitable polymer systems.