A criterion for localization of electron states in disordered materials is presented. Applications to binary alloys, made using the self-energy calculated in the coherent-potential approximation, confirm the Mott-Cohen-Fritzsche-Ovshinsky model in detail. Mobility edges occur inside the band edges. A mobility gap can appear within the band. The band can split into sub-bands, each with mobility edges. Below a critical concentration, an Anderson transition, where the minority sub-band becomes entirely localized, can occur.