Shape-memory polymers (SMPs) are able to perform shape transitions in a pre-defined pathway in response to suitable external stimuli such as heat, magnetism, electricity, moisture, or light. Most of the SMPs are dual-shape materials, which enable a single shape transition from a temporary to a permanent shape. Recently, triple-shape polymers (TSPs), which are capable of accomplishing two shape transitions, as well as multi-shape polymers with shape changes have been introduced including temperature-memory polymers (TMPs) with tunable multiple shape transitions. Different concepts for obtaining multi-shape polymers are introduced and the sophisticated structural design concepts in combination with tailored shape-memory creation processes (SMCPs) are explained. Future opportunities emerge in alternative actuation methods and exploration of potential applications.