The regeneration of 3D tissue constructs with clinically relevant sizes, structures, and hierarchical organizations for translational tissue engineering remains challenging. 3D printing, an additive manufacturing technique, has revolutionized the field of tissue engineering by fabricating biomimetic tissue constructs with precisely controlled composition, spatial distribution, and architecture that can replicate both biological and functional native tissues. Therefore, 3D printing is gaining increasing attention as a viable option to advance personalized therapy for various diseases by regenerating the desired tissues. This review outlines the recently developed 3D printing techniques for clinical translation and specifically summarizes the applications of these approaches for the regeneration of cartilage, bone, and osteochondral tissues. The current challenges and future perspectives of 3D printing technology are also discussed.