Additive manufacturing (AM) is an important technology that led to a high evolution in the manufacture of personalized implants adapted to the anatomical requirements of patients. Due to a worldwide graft shortage, synthetic scaffolds must be developed. Regarding this aspect, biodegradable materials such as magnesium and its alloys are a possible solution because the second surgery for implant removal is eliminated. Magnesium (Mg) exhibits mechanical properties, which are similar to human bone, biodegradability in human fluids, high biocompatibility, and increased ability to stimulate new bone formation. A current research trend consists of Mg-based scaffold design and manufacture using AM technologies. This review presents the importance of biodegradable implants in treating bone defects, the most used AM methods to produce Mg scaffolds based on powder metallurgy, AM-manufactured implants properties, and in vitro and in vivo analysis. Scaffold properties such as biodegradation, densification, mechanical properties, microstructure, and biocompatibility are presented with examples extracted from the recent literature. The challenges for AM-produced Mg implants by taking into account the available literature are also discussed.