Additive Manufacturing (AM) or 3D printing is a manufacturing technique where successive layers of material are layered to produce parts. The design freedom afforded by AM is ideal for the space industry, where part production is low volume and highly customized. The objective of this paper is to review research in the area of Additive Manufacturing For Space (AMFS) in all areas, from propulsion to electronics to printing of habitats, and to identify the gaps and directions in the research. In this paper we investigate the AMFS research by splitting it into two domains: space and ground-based. Space-based AMFS has been performed on the International Space Station using polymers and we also discuss the future of in-space AM, a subject closely related to more general in-space manufacturing. The ground-based research is split into three categories based on the printing material: metal, polymer, and other. The last category includes regolith, cement, and ceramic. This paper explores AMFS by bringing together as much research information as possible using a combination of papers, presentations, and news articles. We expect that the paper will allow the reader to gain an understanding of the current status of AMFS research and will contribute to the field as a reference and research guidelines.