The valence electronic structure of materials with crystalline order is described by the energy—momentum dispersion laws and densities of electron bands. These quantities are directly observed for the surfaces of thin (about 100 Å) solid films by electron momentum spectroscopy, based on kinematically complete observations of ionization events. The principles of the experiment and the imperfections of the probe are described and illustrated by examples. Comparison is made with other electron spectroscopies that measure subsets of the complete energy-momentum density information.