Magnesium-rare earth based alloys are increasingly being investigated due to the formation of highly stable strengthening phases, activation of additional deformation modes and improvement in mechanical properties. Several investigations have been done to study the effect of rare earths when they are alloyed to pure magnesium and other Mg alloys. In this review, the mechanical properties of the previously investigated different magnesium-rare earth based binary alloys, ternary alloys and other higher alloys with more than three alloying elements are presented.