Hydrogels are 3D networks that have a high water content. They have been widely used as cell carriers and scaffolds in tissue engineering due to their structural similarities to the natural extracellular matrix. Among these, "Smart" hydrogels refer to a group of hydrogels that is responsive to various external stimuli such as pH, temperature, light, electric, and magnetic field. Combining the potential of 3D printing and smart hydrogels is an exciting new paradigm in the fabrication of a functional 3D tissue. In this article, we provide a state-of-the-art review on smart hydrogels and bioprinting. We identify the critical material properties needed for the most commonly used bioprinting techniques, namely extrusion-based, inkjet-based, and laser-based techniques. The latest progress in different smart hydrogel systems and their applications in bioprinting are presented. The challenges of printing these hydrogel systems are also highlighted. Lastly, we present the potentials and the future perspectives of smart hydrogels in 3D bioprinting.