Shape memory polymer (SMP) is a typical smart material, which can morph into a temporary shape under specific conditions, and fix the temporary shape under the change of environmental conditions, and can actively return to the initial shape after being stimulated again. In the field of smart manufacturing, the combination of smart material and additive manufacturing technology has given rise to 4D printing technology, realizing the leap forward in the field of 3D printing. The current main development is shape memory polymer 4D printing technology. This paper focused on the realization of 4D printing SMP and characteristics of various stimulus-responsive materials, and then introduced the research on the application of 4D printing structures based on shape memory polymers in the fields of aerospace, biomedicine and flexible robotics, and finally summarized the problems that may be encountered by 4D printing of shape memory polymers in the future and looked forward to its possible future research directions, aiming at letting more people know about 4D printing technology and promoting its application development in various industries.