Magnesium (Mg) alloys possess comparable physical and mechanical properties to bone, making them an outstanding candidate of implant materials for bone fracture treatment. In addition to the excellent biocompatibility, and bioactivity, the engagement of Mg alloys is key for a number of biological functionalities in the human body. The unique biodegradation nature of Mg alloy implants implies that it may not require a secondary removal procedure when the expected supporting tasks accomplish, as they may simply and safely “disappear” over time. Nonetheless, the demonstrated drawback of potentially rapid degradation, is an issue that must be addressed appropriately for Mg implants and is consequently given unique attention in this review article. Herein, the critical criteria and the state-of-the-art strategies for controlling the degradation process of Mg alloys are reported. Furthermore, future developments of biodegradable Mg and its alloys systems with satisfactory specifications for clinical trials and deployment, are discussed. This review aims to provide information to materials scientists and clinical practitioners in the context of developing practical biodegradable Mg alloys.