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Metal-graphene contact is a key interface in graphene-based device applications, and it is known that two types of interfaces are formed between metal and graphene. In this paper, we apply first-principles calculations to twelve metal-graphene interfaces and investigate the detailed interface atomic and electronic structures of physisorption and chemisorption interfaces. For physisorption interfaces (Ag, Al, Cu, Cd, Ir, Pt, and Au), Fermi level pinning and Pauli-exclusion-induced energy-level shifts are shown to be two primary factors determining graphene’s doping types and densities. For chemisorption interfaces (Ni, Co, Ru, Pd, and Ti), the combination of Pauli-exclusion-induced energy-level shifts and hybridized states’ repulsive interactions lead to a band gap opening with metallic gap states. For practical applications, we show that external electric field can be used to modulate graphene’s energy-levels and the corresponding control of doping or energy range of hybridization.