The need for organ and tissue regeneration in patients continues to increase because of a scarcity of donors, as well as biocompatibility issues in transplant immune rejection. To address this, scientists have investigated artificial tissues as an alternative to transplantation. Three-dimensional (3D) bioprinting technology is an additive manufacturing method that can be used for the fabrication of 3D functional tissues or organs. This technology promises to replicate the complex architecture of structures in natural tissue. To date, 3D bioprinting strategies have confirmed their potential practice in regenerative medicine to fabricate the transplantable hard tissues, including cartilage and bone. However, 3D bioprinting approaches still have unsolved challenges to realize 3D hard tissues. In this manuscript, the current technical development, challenges, and future prospects of 3D bioprinting for engineering hard tissues are reviewed.