This article presents a concise overview of modern achievements and existing knowledge gaps in the area of biodegradable magnesium alloys. Hundreds of Mg-based alloys have been proposed as candidates for temporary implants, and this number tends to increase day by day. Therefore, while reviewing common aspects of research in this field, we confine ourselves primarily to the popular Mg-Zn-Ca system, taken as a representative example. Over the last decades, research activities in this area have grown enormously and have produced many exciting results. Aiming at highlighting the areas where research efforts are still scarce, we review the state-of-the-art processing techniques and summarize the functional properties attained via a wide variety of processing routes devised towards achieving a desired properties profile, including the mechanical response in terms of strength, ductility, and fatigue resistance paired with biocompatibility and bio-corrosion resistance or controlled degradability. We pay keen attention to a summary of corrosion properties and mechano-chemical interactions between an aggressive environment and loaded Mg-based structures, resulting in stress corrosion cracking and premature corrosion fatigue failures. The polemic issues and challenges practitioners face in their laboratory research are identified and discussed.