Photoelectron spectroscopy measures the binding energies of electrons in molecules and solids. The article briefly considers experimental methods. A photoelectron spectrum is related to the molecular orbital structure of a system. Variation of the band intensities with photon energy gives information on the atomic orbital content of the originating molecular orbital. Band splitting may have a number of origins such as vibrational states, Jahn–Teller distortions, exchange splittings, and spin–orbit coupling. All of these provide additional information on electronic structure. Density functional calculations of ionization energies give good agreement with experiment. All these points are exemplified throughout and the article concludes with a number of case studies.