The basic concepts in the theory of chemisorption of atoms on metals will be reviewed. The sharp atomic levels of the free atom are broadened into virtual levels by electron tunneling between the atom and the solid. For rapid tunneling, correlation effects on the adatom are weak and a self-consistent field molecular orbital approach is appropriate. The adatom density of states can vary from a Lorentzian level to states split above and below the valence band of the solid, corresponding to the bonding and antibonding orbitals of a surface complex formed between the adatom and its surroundings. The Anderson model treats only Coulomb interactions on the adatom, while the CNDO method of quantum chemistry has been recently employed to include Coulomb interactions in the solid. For strong intra-atomic Coulomb interaction on the adatom, correlation effects are important and the localized magnetic moment on the adatom as predicted by the unrestricted Hartree–Fock approximation is quenched. Correlations have been treated by extended valence bond methods, multiple scattering theory, and configuration mixing techniques. Semiquantitative agreement with experiment is obtained in a number of systems.