Three-dimensional (3D) bioprinting has become a promising strategy for bone manufacturing, with excellent control over geometry and microarchitectures of the scaffolds. The bioprinting ink for bone and cartilage engineering has thus become the key to developing 3D constructs for bone and cartilage defect repair. Maintaining the balance of cellular viability, drugs or cytokines' function, and mechanical integrity is critical for constructing 3D bone and/or cartilage scaffolds. Photo-crosslinkable hydrogel is one of the most promising materials in tissue engineering; it can respond to light and induce structural or morphological transition. The biocompatibility, easy fabrication, as well as controllable mechanical and degradation properties of photo-crosslinkable hydrogel can meet various requirements of the bone and cartilage scaffolds, which enable it to serve as an effective bio-ink for 3D bioprinting. Here, in this review, we first introduce commonly used photo-crosslinkable hydrogel materials and additives (such as nanomaterials, functional cells, and drugs/cytokine), and then discuss the applications of the 3D bioprinted photo-crosslinkable hydrogel scaffolds for bone and cartilage engineering. Finally, we conclude the review with future perspectives about the development of 3D bioprinting photo-crosslinkable hydrogels in bone and cartilage engineering.