Magnesium alloys are the lightest structural metal. The lightness is the main reason for the interest for Mg in various industrial and clinical applications, in which lightweight structures are in high demand. Recent research and developments on magnesium Mg alloys are reviewed. A particular attention is focused on binary and ternary Mg alloys consisting mainly of Al, Zn, Mn, Ca and rare earth (RE) elements. The effects of different alloying elements on the microstructure, the mechanical and the corrosion properties of Mg alloys are described. Alloying induces modifications of the microstructural characteristics leading to strengthening mechanisms, improving then the ductility and the mechanical properties of pure Mg.