In this chapter, we begin by writing out the full reaction rate matrix accounting for the radiative and collisional processes presented in Chapter 34. The radiation field is assumed to originate externally and is thus not in equilibrium with the gas. We then derive the closed-form equilibrium solution for a pure hydrogen gas. Important to achieving equilibrium are the photoionization and recombination timescales. The industry standard ionization code is Cloudy; we describe how one uses this code to create model clouds. Important concepts such as the ionization parameter, cloud ionization structure, and shelf shielding of ionizing photons are discussed in detail. The building of grids of models is explained and example grids showing predictions of ionic column densities and ionization corrections are presented for commonly observed ions. Non-equilibrium collisional ionization models are described, and grids are presented. Sensitivities of the models to variations in the ionizing spectrum are explored. Finally, homology relationships useful for scaling cloud models to infer cloud densities, sizes, masses, and cloud stability are derived.