Four-dimensional (4D) printing is regarded as a methodology that links 3D printing to time, which is characterized by the evolution of predetermined structures or functions for the printed object after applying stimulation. This dynamic feature endows 4D printing the potential to be intelligent, attracting wide attention from academia and industry. The transformation of shape and function is both obtained from the programming of the object endowed by the intrinsic characteristics of the material or by the manufacturing technology. Therefore, it is necessary to understand 4D printing from the perspective of both mechanism and manufacturing. Here, the state-of-the-art 4D printing polymer was summarized, beginning with the classifications, and leading to the mechanisms, stimulations, and technologies. The links and differences between 4D printing polymer and shape memory polymer, between 4D printing and 3D printing were highlighted. Finally, the biomedical applications were outlined and the perspectives were discussed.