This century is blessed with enhanced medical facilities on the grounds of the development of smart biomaterials. The rise of the four-dimensional (4D) bioprinting technology is a shining example. Using inert biomaterials as the bioinks for the three-dimensional (3D) printing process, static objects that might not be able to mimic the dynamic nature of tissues would be fabricated; by contrast, 4D bioprinting can be used for the fabrication of stimuli-responsive cell-laden structures that can evolve with time and enable engineered tissues to undergo morphological changes in a pre-planned way. For all the aptitude of 4D bioprinting technology in tissue engineering, it is imperative to select suitable stimuli-responsive biomaterials with cell-supporting functionalities and responsiveness; as a result, in this article, recent advances and challenges in smart biomaterials for 4D bioprinting are briefly discussed. An overview perspective concerning the latest developments in 4D-bioprinting is also provided.