Tremendous advances in tissue engineering and regenerative medicine have revealed the potential of fabricating biomaterials to solve the dilemma of bone and articular defects by promoting osteochondral and cartilage regeneration. Three-dimensional (3D) bioprinting is an innovative fabrication technology to precisely distribute the cell-laden bioink for the construction of artificial tissues, demonstrating great prospect in bone and joint construction areas. With well controllable printability, biocompatibility, biodegradability, and mechanical properties, hydrogels have been emerging as an attractive 3D bioprinting material, which provides a favorable biomimetic microenvironment for cell adhesion, orientation, migration, proliferation, and differentiation. Stem cell-based therapy has been known as a promising approach in regenerative medicine; however, limitations arise from the uncontrollable proliferation, migration, and differentiation of the stem cells and fortunately could be improved after stem cells were encapsulated in the hydrogel. In this review, our focus was centered on the characterization and application of stem cell-laden hydrogel-based 3D bioprinting for bone and cartilage tissue engineering. We not only highlighted the effect of various kinds of hydrogels, stem cells, inorganic particles, and growth factors on chondrogenesis and osteogenesis but also outlined the relationship between biophysical properties like biocompatibility, biodegradability, osteoinductivity, and the regeneration of bone and cartilage. This study was invented to discuss the challenge we have been encountering, the recent progress we have achieved, and the future perspective we have proposed for in this field.