The structure and electronic properties of graphene are fundamental to those of carbon materials and are significantly influenced by the presence of nonideal structures such as defects, impurities, and edges, which can be controlled through the functionalization of graphene by chemical species. According to the energy scale of the interactions between graphene and these species, three routes for the functionalization of graphene were examined: the proximity effects of adsorbed molecules, ion irradiation, and covalent bonding. The sign and concentration of the charge carrier, and its scattering in graphene were precisely controlled by the adsorption of molecules on it or the chemical modification of the surface of the supporting substrate. Irradiation with an ion beam modified the electronic structure of graphene and its electrical conductivity in a well-defined manner. Direct chemical modification induced the formation of covalent bonds with guest species and significantly changed the topology of the honeycomb lattice of graphene, resulting in localized spin magnetism and catalytic activity originating from spin-polarized localized states emerging at the Fermi energy.