AbstractShape-memory polymers (SMP) are an emerging class of active materials, which are able to change their shape in a predefined way upon appropriate stimulation. SMP, which can switch from a temporary to their permanent shape, are dual-shape materials. Here fundamental aspects concerning the design of suitable polymer architectures as well as of tailored programming processes are presented. Furthermore, the influence of various physical parameters on the shape recovery is discussed. Shape-memory research initially was focused on the thermally induced dual shape-effect. Presently, this research field is rapidly developing in two major areas. On the one hand other stimuli are being realized by either indirect thermal actuation or direct actuation by addressing stimuli-sensitive groups on the molecular level. On the other hand the programmed shape changes are getting more complex. Triple-shape materials are able to perform two subsequent on-demand shape changes and multishape materials are extending this to even more steps.