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The electronic properties of single-crystalline films of monolayer hexagonal boron nitride (h-BN) formed on Ni(111), Pd(111), and Pt(111) are reviewed. From the comparison of the present data with those for the rare-gas solids on metal surfaces, the interaction between the BN film and the metal substrate has been assigned to be physisorption. The valence- and conduction-band structures of the monolayer h-BN are almost independent of the substrate. The energy bands and core-levels in the BN film align with respect to the vacuum level, not to the Fermi level. In accord with these ground-state properties of the BN/metal system, the observed excitation energies for interband transitions change from one substrate to the other depending on the work function.