The increased demand for alloys that can serve as implantation devices with outstanding bio-properties has led to the development of numerous biomedical Mg-based alloys. These alloys have been extensively investigated for their performance in living tissue with mixed results. Hence, there are still major concerns regarding the use of magnesium alloys for such applications. Among the issues raised are elevated corrosion rates, hydrogen generation, and the maintenance of mechanical integrity for designated healing times. In addition, toxicity can arise from the addition of alloying elements that are intended to improve the mechanical integrity and corrosion resistance of Mg alloys. The current work reviews the recent advances in the development of Mg alloys for applications as bio-absorbable materials in living organic environments. In particular, it attempts to develop a roadmap of effective factors that can be utilized when designing Mg alloys. Among the factors reviewed are the effects of alloying additions and processing methods on the exhibited mechanical properties and corrosion rates in simulated bio-fluids used in biomedical applications.