Four-dimensional (4D) bioprinting, encompassing a wide range of disciplines including bioengineering, materials science, chemistry, and computer sciences, is emerging as the next-generation biofabrication technology. By utilizing stimuli-responsive materials and advanced three-dimensional (3D) bioprinting strategies, 4D bioprinting aims to create dynamic 3D patterned biological structures that can transform their shapes or behavior under various stimuli. In this review, we highlight the potential use of various stimuli-responsive materials for 4D printing and their extension into biofabrication. We first discuss the state of the art and limitations associated with current 3D printing modalities and their transition into the inclusion of the additional time dimension. We then suggest the potential use of different stimuli-responsive biomaterials as the bioink that may achieve 4D bioprinting where transformation of fabricated biological constructs can be realized. We finally conclude with future perspectives.