Various techniques for the spectroscopy of interfaces are discussed such as core level spectroscopy, near-edge absorption, and optical second harmonic generation. The CaF2/Si(111) interface serves as a model for determining electronic states at an interface. A pair of interface states is found, one occupied, the other empty. They represent the bonding (antibonding) combinations of the orbitals that hold the interface together. The interface layer exhibits new properties, e.g., more than twice the band gap of bulk Si. The bonding at complex interfaces, such as SiO2/Si, can also be analyzed using the simple relation between core level shift and oxidation state. Only models with an extended interface are compatible with the observed distribution of intermediate oxidation states. © 1989.