Recently, three-dimensional (3D) printing of biological tissues and organ has become an attractive interdisciplinary research topic that combines a broad range of fields including engineering, biomaterials science, cell biology, physics, and medicine. The 3D bioprinting can be used to produce complex tissue engineering scaffolds based on computer designs obtained from patient-specific anatomical data. It is a powerful tool for building structures by printing cells together with matrix materials and biochemical factors in spatially predefined positions within confined 3D structures. In the field of the 3D bioprinting, three major categories of the 3D bioprinting include the stereolithography-based, inkjet-based, and dispensing-based bioprinting. Some of them have made significant process. Each technique has its own advantages and limitations. Compared with non-biological printing, the 3D bioprinting should consider additional complexities: biocompatibility, degradability of printing materials, cell types, cell growth, cell viability, and cell proliferation factors. Numerous 3D bioprinting technologies have been proposed, and some of them have been making great progress in printing several tissues including multilayered skin, cartilaginous structures, bone, vasculature even heart and liver. This review summarizes basic principles and key aspects of some frequently utilized printing technologies, and introduces current challenges, and prospects in the 3D bioprinting.