This chapter discusses the theoretical modeling of impact ionization and avalanche generation in GaN materials and devices from a charge transport perspective. New analytical expressions are developed for particle densities and current densities in the local approximation. Nonlocal aspects of charge transport are discussed, and new analytic solutions to the Boltzmann transport equation are presented which provide insight into the relaxation of carriers injected into regions of homogeneous and inhomogeneous electric fields. The inference of avalanche coefficients from measurement is shown to be complicated by considerations of nonlocality and ionization feedback. Shortcomings of semi-analytic approaches to modeling avalanche current addressing the issue of dead space are revealed. Original expressions relating ionization coefficients to carrier multiplication factors are presented for the limiting case of multiplication regions with uniform field.