Constructing scaffolds with the desired structures and functions is one of the main goals of tissue engineering. Three-dimensional (3D) bioprinting is a promising technology that enables the personalized fabrication of devices with regulated biological and mechanical characteristics similar to natural tissues/organs. To date, 3D bioprinting has been widely explored for biomedical applications like tissue engineering, drug delivery, drug screening, and in vitro disease model construction. Among different bioinks, photocrosslinkable bioinks have emerged as a powerful choice for the advanced fabrication of 3D devices, with fast crosslinking speed, high resolution, and great print fidelity. The photocrosslinkable biomaterials used for light-based 3D printing play a pivotal role in the fabrication of functional constructs. Herein, this review outlines the general 3D bioprinting approaches related to photocrosslinkable biomaterials, including extrusion-based printing, inkjet printing, stereolithography printing, and laser-assisted printing. Further, the mechanisms, advantages, and limitations of photopolymerization and photoinitiators are discussed. Next, recent advances in natural and synthetic photocrosslinkable biomaterials used for 3D bioprinting are highlighted. Finally, the challenges and future perspectives of photocrosslinkable bioinks and bioprinting approaches are envisaged.