Publisher Summary This chapter describes the theoretical information that is available on isolated, interstitial hydrogen and muonium in crystalline semiconductors. Theoretical techniques for studying impurities in semiconductors can be categorized according to the following two criteria: the geometrical arrangement and the method for treating the electron–electron interactions that are used for the study of impurities in semiconductors. The information that can be obtained may be categorized as follows: (1) the location of the impurity (from total energy surfaces), (2) its electronic structure (for example, band structure, spin density, and hyperfine parameters), and (3) possible charge states. As an example of the computational results, theory demonstrates, in agreement with experiment, that the most stable location for isolated (neutral) hydrogen and muonium in silicon (Si), diamond, and GaAs is the bond-center site, and this is a consequence of a large lattice relaxation that permits the formation of a three-center bond. The bond-center site, where the electron density is highest, is also the stable location for isolated hydrogen in its positive charge state.