Selective laser melting (SLM) is an additive manufacturing method with rapid solidification properties, which is conducive to the preparation of alloys with fine microstructures and uniform chemical compositions. Magnesium alloys are lightweight materials that are widely used in the aerospace, biomedical and other fields due to their low density, high specific strength, and good biocompatibility. However, the poor laser formability of magnesium alloy restricts its application. This paper discusses the current research status both related to the theoretical understanding and technology applications. There are problems such as limited processable materials, immature process conditions and metallurgical defects on SLM processing magnesium alloys. Some efforts have been made to solve the above problems, such as adding alloy elements and applying postprocessing. However, the breakthroughs in these two areas are rarely reviewed. Due to the paucity of publications on postprocessing and alloy design of SLMed magnesium alloy powders, we review the current state of research and progress. Moreover, traditional preparation techniques of magnesium alloys are evaluated and related to the SLM process with a view to gaining useful insights, especially with respect to the postprocessing and alloy design of magnesium alloys. The paper also reviews the influence of process parameters on formability, densification and mechanical behavior of magnesium. In addition, the progress of microstructure and metallurgical defects encountered in the SLM processed parts is described. Finally, this article summarizes the research results, and with respect to materials and metallurgy, the new challenges and prospects in the SLM processing of magnesium alloy powders are proposed with respect to alloy design, base material purification, inclusion control and theoretical calculation, and the role of intermetallic compounds.