With the advances of stem cell research, development of intelligent biomaterials and three-dimensional biofabrication strategies, highly mimicked tissue or organs can be engineered. Among all the biofabrication approaches, bioprinting based on inkjet printing technology has the promises to deliver and create biomimicked tissue with high throughput, digital control, and the capacity of single cell manipulation. Therefore, this enabling technology has great potential in regenerative medicine and translational applications. The most current advances in organ and tissue bioprinting based on the thermal inkjet printing technology are described in this review, including vasculature, muscle, cartilage, and bone. In addition, the benign side effect of bioprinting to the printed mammalian cells can be utilized for gene or drug delivery, which can be achieved conveniently during precise cell placement for tissue construction. With layer-by-layer assembly, three-dimensional tissues with complex structures can be printed using converted medical images. Therefore, bioprinting based on thermal inkjet is so far the most optimal solution to engineer vascular system to the thick and complex tissues. Collectively, bioprinting has great potential and broad applications in tissue engineering and regenerative medicine. The future advances of bioprinting include the integration of different printing mechanisms to engineer biphasic or triphasic tissues with optimized scaffolds and further understanding of stem cell biology.