As one of the lightest metal materials, Mg alloys have a broad application prospect, and it has been one of the focuses to develop advanced Mg alloys at present. First-principles calculation provides a cost-effective method for development and design of advanced Mg alloys. Based on first-principles calculation methods, researches on intermetallic compounds and solid solutions of Mg alloys are reviewed. The research work on crystal structure, elastic constant, elastic modulus and generalized stacking fault energy of Mg alloys by first-principles calculation is introduced,and the effects of alloying elements and phase structures on mechanical properties of Mg alloys are also discussed, aiming to to illustrate that the first-principles computation plays an important role in the development of Mg alloys. And we hope that it could provide a theoretical reference for composition design and performance optimization of advanced Mg alloys.