The study of superhard materials plays a critical role in mode industrial applications due to their widespread applications as cutting tools,abrasives,exploitation drills,and coatings.The search for new superhard materials with superior performance remains a hot topic and is mainly considered as two classes of materials:(i) the light-element compounds in the B-C-N-O(-Si) system with strong and short covalent bonds,and (ii) the transition-element light-element compounds with strong covalent bonds frameworks and high valence electron density.In this paper,we review the recent achievements in the prediction of superhard materials mostly using the advanced CALYPSO methodology.A number of novel,superhard crystals of light-element compounds and transition-metal borides,carbides,and nitrides have been theoretically identified and some of them account well for the experimentally mysterious phases.To design superhard materials via CALYPSO methodology is independent of any known structural and experimental data,resulting in many remarkable structures accelerating the development of new superhard materials.