Disorder profoundly affects excitation transport in solids. Plane wave solutions lose relevancy, and marked departures from conventional band transport can occur. In particular, in the limit of strong disorder, the wave functions of an otherwise pure crystal become localized. At zero temperature, transport becomes impossible. As the temperature is raised, inelastic processes can make up the energy mismatch between sites introduced by the disorder, allowing spatial transfer to occur. The purpose of this chapter is to examine those mechanisms which depend on thermal motion of the lattice. This “phonon-assisted transport” is responsible for a variety of conduction processes, from electrical conductivity to exciton diffusion. We shall treat the extreme limit of localization in this chapter, namely an excitation localized on an optical site. The reasons for the localization and the character of localized states will be briefly outlined in Sect. 2.1; the nature of phonon-assisted excitation transfer is discussed in Sect. 2.2; and explicit calculations developed for the transfer rates for multipolar site—site coupling in Sect. 2.3 and for phonon-assisted radiative transport in Sect. 2.4. Section 2.5 presents a short discussion of the reverse: resonantly trapped phonons which can escape the trapping volume because of spectral energy transport. Our results are summarized in Sect. 2.6.