A review is presented of the current research and development of shape-memory materials, including shape-memory alloys, shape-memory ceramics and shape-memory polymers. The shape-memory materials exhibit some novel performances, such as sensoring (thermal, stress or field), large-stroke actuation, high damping, adaptive responses, shape memory and superelasticity capability, which can be utilized in various engineering approaches to smart systems. Based on an extensive literature survey, the various shape-memory materials are outlined, with special attention to the recently developed or emerged materials. The basic phenomena in the materials, that is, the stimulus-induced phase transformations which result in the unique performance and govern the remarkable changes in properties of the materials, are systematically lineated. The remaining technical barriers, and the challenges to improve the present materials system and develop a new shape memory materials are discussed.