Selective Laser Melting (SLM) of magnesium alloys is the technology undergoing dynamic development in many research centres. The results are promising and make it possible to manufacture defect-free material with better properties than those offered by the manufacturing technologies used to date. This review aims to evaluate present state as well as main challenges of using Laser Powder Bed Fusion (L-PBF) for processing magnesium alloys as an alternative way to conventional technologies to manufacture parts in the aerospace industry. This literature review is the first one to outline information concerning the potential to use magnesium alloys in the aerospace industry as well as to summarise the results of magnesium alloy processing using AM technologies, in particular L-PBF. The available literature was reviewed to gather information about: the use of magnesium alloys in the aerospace industry—the benefits and limitations of using magnesium and its alloys, examples of applications using new processing methods to manufacture aerospace parts, the benefits and potential of using L-PBF to process metallic materials, examples of the use of L-PBF to manufacture aerospace parts, and state-of-the-art research into L-PBF processing of magnesium and magnesium alloys.