Three-dimensional (3D) bioprinting is a rapidly growing technology that has been widely used in tissue engineering, disease studies, and drug screening. It provides the unprecedented capacity of depositing various types of biomaterials, cells, and biomolecules in a layer-by-layer fashion, with precisely controlled spatial distribution. This technology is expected to address the organ-shortage issue in the future. In this review, we first introduce three categories of 3D bioprinting strategies: inkjet-based printing (IBP), extrusion-based printing (EBP), and light-based printing (LBP). Biomaterials and cells, which are normally referred to as 'bioinks,' are then discussed. We also systematically describe the recent advancements of 3D bioprinting in fabricating cell-laden artificial tissues and organs with solid or hollow structures, including cartilage, bone, skin, muscle, vascular network, and so on. The development of organs-on-chips utilizing 3D bioprinting technology for drug discovery and toxicity testing is reviewed as well. Finally, the main challenges in current studies and an outlook of the future research of 3D bioprinting are discussed.