Magnesium alloys such as AZ91 have received much attention due to their attractive properties, including biocompatibility and lightness. Although magnesium is a potential candidate for implant application, due to its rapid degradation in the physiological environment, there are still some challenges to using it as biocompatible implants. In this regard, various techniques such as microstructure modification and coating are utilized to moderate the degradation rate of magnesium alloys. Therefore, efforts are being made to conduct more extensive research to produce magnesium implants with acceptable corrosion resistance. In this literature review, an overview of the history of research on the corrosion behavior, biodegradability, microstructure deformation mechanisms, crystallographic texture in magnesium alloys with a focus on AZ91 Mg alloy, is provided. In addition, the necessity of improving the properties of AZ91 Mg alloy by the two methods of improving microstructure and coating, and existing innovations in these methods are investigated.