This article provides an overview of the findings and production processes for the mineral materials that have been developed and tested worldwide in the past with regard to the establishment of a lunar base. Firstly, the aim of and procedure for constructing a lunar base are briefly outlined. Following that, the lunar environment factors and their influence on a possible structure are described. The paper then presents the advantages and disadvantages of the materials examined, such as sulphur concrete, cast basalt, lunar concrete or polymer concrete, on the one hand, as well as production processes investigated previously, such as sintering, geothermite reaction and 3D printing, on the other. One promising method is the dry-mix/steam-injection (DMSI) method for producing a lunar concrete as a possible material which was developed by T. D. Lin and is based on cement made from lunar resources.