The latest progress in shape-memory polymers was summarized and reviewed in this paper. The principle of shape memory effect was analyzed from the point of polymer structure. Cross-linked polyolefin shape memory polymers have chemical cross-linking and semi-crystalline structures. Inversely,shape memory effects of polyurethane are ascribed to its physical cross-linking networks and phase separation structure. And,shape memory effects of liquid crystal elastomer come from phase transition of liquid crystal states. The characteristics and applications in morphing aircraft and self-deployable space structures of some shape-memory polymers such as shape memory polyurethane,elastic shape memory composites and the likes were also introduced and prospected.