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The unusual electronic structure of graphene characterized by linear energy dispersion of bands adjacent to the Fermi level underpins its remarkable transport properties. However, for practical device integration, graphene will need to be interfaced with other materials: 2D layered structures, metals (as ad-atoms, nanoparticles, extended surfaces, and patterned metamaterial geometries), dielectrics, organics, or hybrid structures that in turn are constituted from various inorganic or organic components. The structural complexity at these nanoscale interfaces holds much promise for manifestation of novel emergent phenomena and provides a means to modulate the electronic structure of graphene. In this feature article, we review the modifications to the electronic structure of graphene induced upon interfacing with disparate types of materials with an emphasis on iterative learnings from theoretical calculations and …