Additive manufacturing has transformed the perspective of producing three dimensions (3D) objects toward achieving high quality in terms of accuracy, resolution, and high mechanical integrity with excellent surface finishing in little time compared to subtractive (traditional) production. Vat photopolymerization (VPP) additive manufacturing is among the most common 3D printing technology used in the medical field, academic research, and industrial production of 3D parts. Four main 3D printing techniques fall under VPP, namely continuous liquid interface production (CLIP), daylight polymer printing (DPP), stereolithography (SLA), and digital light processing (DLP). The last two are the focus of the present article. The high accuracy, precision, the unique ability to produce highly complex porous structural geometries, the low printing cost, and the production time of 3D structures compared to subtractive 3D manufacturing make DLP and SLA suitable for medical applications, specifically in regenerative medicine. This review presents the recent trend of DLP and SLA as used in medical research related to bone tissue engineering highlighting the mechanical and biological properties of the resulting 3D bone structures. In addition, photopolymerization mechanisms, photocurable materials, and the working principles of DLP and SLA are introduced.