Recent advances have allowed for three-dimensional (3D) printing technologies to be applied to biocompatible materials, cells and supporting components, creating a field of 3D bioprinting that holds great promise for artificial organ printing and regenerative medicine. At the same time, stem cells, such as human induced pluripotent stem cells, have driven a paradigm shift in tissue regeneration and the modeling of human disease, and represent an unlimited cell source for tissue regeneration and the study of human disease. The ability to reprogram patient-specific cells holds the promise of an enhanced understanding of disease mechanisms and phenotypic variability. 3D bioprinting has been successfully performed using multiple stem cell types of different lineages and potency. The type of 3D bioprinting employed ranged from microextrusion bioprinting, inkjet bioprinting, laser-assisted bioprinting, to newer technologies such as scaffold-free spheroid-based bioprinting. This review discusses the current advances, applications, limitations and future of 3D bioprinting using stem cells, by organ systems.