3D bioprinting has developed tremendously in the last couple of years and enables the fabrication of simple, as well as complex, tissue models. The international space agencies have recognized the unique opportunities of these technologies for manufacturing cell and tissue models for basic research in space, in particular for investigating the effects of microgravity and cosmic radiation on different types of human tissues. In addition, bioprinting is capable of producing clinically applicable tissue grafts, and its implementation in space therefore can support the autonomous medical treatment options for astronauts in future long term and far-distant space missions. The article discusses opportunities but also challenges of operating different types of bioprinters under space conditions, mainly in microgravity. While some process steps, most of which involving the handling of liquids, are challenging under microgravity, this environment can help overcome problems such as cell sedimentation in low viscous bioinks. Hopefully, this publication will motivate more researchers to engage in the topic, with publicly available bioprinting opportunities becoming available at the International Space Station (ISS) in the imminent future.