Most of our knowledge of the electronic structure of atoms and molecules is derived from excitation energies and transition probabilities. These observable quantities are related to the electronic wave functions by integrals over unmeasured variables. Another observable more directly related to the wave function than energy or transition probability is the single-electron momentum density, the probability that an electron in a well-defined orbital has a given value of momentum. Over the last twenty years a technique has been developed for measuring momentum densities in atoms and molecules. The technique, ($e$,$2e$) spectroscopy, is based on electron-impact ionization with complete determination of the momentum of both incoming and outgoing electrons. The conditions necessary to extract momentum-density information from the ionization experiments are examined and related to general theories of electron scattering. Different experimental arrangements are reviewed and momentum-density results from selected examples are discussed.

DOI:https://doi.org/10.1103/RevModPhys.66.985