Nature's materials have evolved over time to be able to respond to environmental stimuli by generating complex structures that can change their functions in response to distance, time, and direction of stimuli. A number of technical efforts are currently being made to improve printing resolution, shape fidelity, and printing speed to mimic the structural design of natural materials with three-dimensional (3D) printing. Unfortunately, this technology is limited by the fact that printed objects are static and cannot be reshaped dynamically in response to stimuli. In recent years, several smart materials have been developed that can undergo dynamic morphing in response to a stimulus, thus resolving this issue. Four-dimensional (4D) printing refers to a manufacturing process involving additive manufacturing, smart materials, and specific geometries. It has become an essential technology for biomedical engineering and has the potential to create a wide range of useful biomedical products. This paper will discuss the concept of 4D bioprinting and the recent developments in smart matrials, which can be actuated by different stimuli and be exploited to develop biomimetic materials and structures, with significant implications for pharmaceutics and biomedical research, as well as prospects for the future.