Shape memory polymer is a kind of intelligent material which can change shapes under the stimulation of external environment. The advent of 4D printing technology promotes the development of smart materials and brings new opportunities for further research in the fields of minimally invasive medical, intelligent robots, flexible electronics and other high-tech industries. In this paper, the emerging and development as well as five new polymer printing technologies of 4D printing technology are introduced firstly. Then, the research progress of shape memory polymers and their composites are demonstrated in the perspectives of thermal, electrical, magnetic and optical driving. Next, we summarize the preparation and properties of shape memory polymers and their composites, as well as the potential applications of the printed structures in biomedical, aerospace, intelligent devices and biomimetic fields. Finally, the problems of 4D printing are pointed out in four aspects of technology, material, driving mode and application verification and the future research directions are discussed.