Graphene/metal oxide and sulphide nanocomposites have been widely studied as anode materials for lithium ion batteriesand exhibit excellent electrochemical properties, due to the synergistic effect between graphene and metal oxide andsulfide. Based on the first-principles total energy calculations, it is revealed that interfacial oxygen atoms play an important roleon the interfacial lithium storage of G/TiO2. Surface and interfacial lithium storage via an electrostatic capacitive mechanismcontributes significantly to the electrode capacity. In graphene/metal sulphide nanocomposites, Li adsorption energies atinterfaces are larger than that on the corresponding metal sulphide surfaces with almost no enhancement of the energy barriersfor Li atom diffusion. The enhanced Li adsorption capability at Li2S/G interface contributes to the extra storage capacity ofgraphene/metal sulphide composites. Thereby, a smart composite consisting of sandwich-like nanosheets with uniform MoS2@carbon-coated ultrathin TiO2 nanosheets has been constructed through facile hydrothermal method to enhance the cycling andrate performances of MoS2. In this uniform sandwich-like structure, carbon-coated ultrathin TiO2 is conformably embeddedby MoS2 shells via intimate interfacial contacts, while the carbon coats TiO2 via Ti-O-C bonds. Due to the abundant interfacesin the composites, as well as the high structure stability of TiO2 during charge and discharge cycles, high-performance of thelithium-ion battery anode material is obtained.