Wrought magnesium alloys attract special interests as lightweight structural material due to their homogeneous microstructure and enhanced mechanical properties compared to as-cast alloys. In this contribution, recent research and developments on wrought magnesium alloys are reviewed from the viewpoint of the alloy design, focusing on Mg-Al, Mg-Zn and Mg-rare earth (RE) systems. The effects of different alloying elements on the microstructure and mechanical properties are described considering their strengthening mechanisms, e.g. grain refinement, precipitation and texture hardening effect. Finally, the new alloy design and also the future research of wrought magnesium alloys to improve their mechanical properties are discussed.