Stem cells offer tremendous promise for regenerative medicine as they can become a variety of cell types. They also continuously proliferate, providing a renewable source of cells. Recently, it has been found that 3D printing constructs using stem cells, can generate models representing healthy or diseased tissues, as well as substitutes for diseased and damaged tissues. Here, we review the current state of the field of 3D printing stem cell derived tissues. First, we cover 3D printing technologies and discuss the different types of stem cells used for tissue engineering applications. We then detail the properties required for the bioinks used when printing viable tissues from stem cells. We give relevant examples of such bioprinted tissues, including adipose tissue, blood vessels, bone, cardiac tissue, cartilage, heart valves, liver, muscle, neural tissue, and pancreas. Finally, we provide future directions for improving the current technologies, along with areas of focus for future work to translate these exciting technologies into clinical applications.