▎ 摘　　要

Recent progress in the theoretical research on the band structures of perfect, defective and doped graphenes is reviewed. The relationship between the quantum capacitance of graphenes in supercapacitors and their band structures is analyzed. Electronic interactions and the diffusion behavior of Li ionsin different graphenestructures in lithium ion batteries are summarized. The role of different structures in the oxygen reduction reaction in the lithium-air battery is elaborated. This theoretical research lays a solid foundation for new ideas for novel graphene-based energy storage devices.