Magnesium (Mg) and Mg alloys are considered as potential candidates for biomedical applications because of their high specific strength, low density, and elastic modulus, degradability, good biocompatibility and biomechanical compatibility. However, the rapid corrosion rate of Mg alloys results in premature loss of mechanical integrity, limiting their clinical application in load-bearing parts. Besides, the low strength of Mg alloys restricts their further application. Thus, it is essential to understand the characteristics and influencing factors of mechanical and corrosion behavior, as well as the methods to improve the mechanical performances and corrosion resistance of Mg alloys. This paper reviews the recent progress in elucidating the corrosion mechanism, optimizing the composition, and microstructure, enhancing the mechanical performances, and controlling the degradation rate of Mg alloys. In particular, the research progress of surface modification technology of Mg alloys is emphasized. Finally, the development direction of biomedical Mg alloys in the future is prospected.