The theory of neutral particle kinetics treats the transport of mass, momentum, and energy in a plasma due to neutral particles that themselves are unaffected by magnetic fields. This transport affects the global power and particle balances infusion devices, as well as profile control and plasma confinement quality, particle and energy fluxes onto device components, performance of pumping systems, and the design of diagnostics and the interpretation of their measurements. The development of analytic, numerical, and Monte Carlo methods of solving the time-independent Boltzmann equation describing neutral kinetics is reviewed. These models for neutral particle behavior typically use adaptations of techniques developed originally for computing neutron transport, due to the analogy between the two phenomena, where charge-exchange (CX) corresponds to scattering and ionization to absorption. There are, however, some important qualitative differences between the two fields. Progress in the simulation of neutral kinetics depends on developing multidimensional analytic methods and obtaining experimental data for the physical processes of wall reflection, the neutral/plasma interaction, and for processes in fusion devices that are directly related to neutral transport, such as Hα emission rates, plenum pressures, and CX emission spectra.