Mg alloys have been widely used in aerospace and other fields because of its low density, light-weighting effects and abundant mineral resources. It has become a“ new green material of the 21st century”. However, Mg has strong electrochemical activity and is prone to corrosion, which has been limiting the wide application of magnesium alloys. At present, exploring the corrosion mechanism of Mg alloys and designing the composition of corrosion-resistant Mg alloys have attracted world-wide attention. This review discusses the research progress on the design of corrosion resistant of Mg alloys. It mainly describes the corrosion mechanism of Mg alloy and anomalous hydrogen reaction phenomenon, as well as the corrosion types such as galvanic corrosion, pitting corrosion, exfoliation corrosion and stress corrosion. And the effects of different alloying elements on the corrosion resistance of Mg alloy are summarized. Focuses on the application of firstprinciples, molecular dynamics, and X-CT technology in Mg alloy corrosion, which is expected to provide principles for the chemistry design of corrosion-resistant Mg alloys.