Inverse photoemission (or bremsstrahlung spectroscopy) is the time-reversed photoemission process. Electronic states are probed via radiative transitions of an incoming electron into unoccupied states. X-ray bremsstrahlung spectroscopy is a well-established technique but its extension to the ultraviolet (with electrons incident at about 4–30 eV energy) has only begun recently. With lower electron energies the surface sensitivity increases such that monolayers can be probed. Also, the momentum of electrons in a solid can be determined by angle-resolved inverse photoemission, i.e., energy band dispersions can be mapped. Unoccupied electronic states play an important role, e.g., in ferromagnetism (minority spin states), in chemisorption (electron acceptor states of adsorbates), and for semiconductors (conduction by electrons). A status report is given of the mapping of bulk energy bands, and the observation of surface states. Recent data from SiO2 are used to make the connection with luminescence.