The previous chapters are concerned with the structure and the density of states distribution of a-Si: H, describing the effects of growth, doping and defect reactions. The remainder of the book addresses the various electronic phenomena which result from the electronic structure. Foremost amongst these properties is the electrical conductivity, σ. The distinction between localized and extended electronic states is one of the fundamental concepts in the study of amorphous semiconductors. At zero temperature, carriers in extended states are conducting, but in localized states are not. Most of the experimental measurements of the localized state distribution rely on this property. Although both the concept of electrical conduction and its measurement seem simple, it is a complex process. The conductivity is a macroscopic quantity which represents an average property of the carriers as they move from site to site. The calculation of the conductivity therefore involves the transfer rate, scattering and trapping processes, as well as the appropriate average over the distribution of states. The averaging due to the disorder is the most difficult and leads to many of the interesting effects. The theory of conductivity near a mobility edge in disordered systems has been debated for many years and is still not completely agreed. The theory has applications beyond the boundaries of amorphous semiconductors, for example, in doped crystals, amorphous metals and low-dimensional materials. The discussion of the theory in this book is necessarily abbreviated and describes only the main ideas and how they apply to a-Si:H.