The present manuscript summarizes the modern view on the problem of the graphene-metal interaction. Presently, the close-packed surfaces of d metals are used as templates for the preparation of highly-ordered graphene layers. Different classifications can be introduced for these systems: graphene on lattice-matched and graphene on lattice-mismatched surfaces where the interaction with the metallic substrate can be either "strong" or "weak". Here these classifications, with the focus on the specific features in the electronic structure in all cases, are considered on the basis of large amount of experimental and theoretical data, summarized and discussed. The perspectives of the graphene-metal interfaces in fundamental and applied physics and chemistry are pointed out.