Hexagonal boron nitride (h - BN) is the isoelectronic but insulating counterpart of graphene. Like graphene it can easily be grown as high-quality nanotubes or as single layers on metal surfaces. Both materials can be exfoliated or transferred after single-layer growth from suitable substrates onto new surfaces. In view of electronic devices or optical sensors, for instance, the carrier dynamics in the conduction bands determine the device properties. The band edge of the unoccupied band structure of h - BN is dominated by two kinds of states, free-electron-like interlayer or interface states and a flat conduction band valley derived from π*-states. The measurement of excited states and excited-state lifetimes in is the main topic of the present article with a special focus on the dynamics close to the gamma point. While the π* conduction band minimum is strongly localised at the boron sites, the charge density of free-electron-like states is outside the planes and is likely to be important for interactions like charge transfer with adjacent layers and substrates. We will review previous efforts to determine the nature of the bandgap and the band structure of unoccupied states with particular emphasis on but not restricted to single-layer h - BN  epitaxially grown on a Ni(1 1 1) surface.