Graphene is emerging as a new material for future applications in electronics, mechanics, optics, and energy. Recently, catalytic chemical vapor deposition (CVD) growth has attracted considerable interest as an effective means of producing large-area graphene films with relatively low cost. However, because most of the CVD growth has been done over polycrystalline metal films or foils, as-grown graphene has relatively small grain size and its orientation is not controlled. Here, I present our recent studies on our epitaxial CVD growth of graphene using the crystalline metal films deposited on sapphire c-plane and MgO substrates. The domain structure is discussed in terms of crystalline plane dependence of the catalyst Cu film. Further development of this epitaxial graphene film to fabricate nanoribbon structures as well as the catalytic growth of graphene nanoribbons is also demonstrated.