To overcome the limitation of two-dimensional cell culture not being able to mimic the in vivo microenvironment, three-dimensional (3D) bioprinting technology for 3D cell culture has emerged as an innovative culture platform. 3D bioprinting technologies can be divided into five types: inkjet-based bioprinting, extrusion-based bioprinting, stereolithography bioprinting, laser-assisted bioprinting and digital laser processing-based bioprinting technology. The 3D printing strategies achieved through a combination of these technologies can be applied to develop tissue regeneration, drug evaluation and drug delivery systems. In addition, the choice of cells and biomaterials is an important factor in fabricating tissue/organ models. Biomaterials for 3D bioprinting can be divided into natural polymers (alginate, gelatin, collagen, chitosan, agarose, and hyaluronic acid) and synthetic polymers (polylactic acid, polyvinyl alcohol, polycaprolactone, polyethylene oxide and thermoplastic polyurethane). Depending on the goals of 3D bioprinting experiments, biomaterials can be used alone or in combination with various polymers. 3D bioprinting technology has the potential to be applied for personalized medicine, precision medicine and the fabrication of artificial tissue/organs.