Chemical processes are central to the comprehension of rocket and missile exhaust structure. Afterburning of superstoichiometric, reduced products drives heating beyond the nozzle. Trace metals can suppress radical cycling intensities and simultaneously act as the source of ionization. Particles inorganic and otherwise undergo fluid slip and thereby impact heat and momentum budgets. All radiation interactions of the plume are intimately coupled into this rich chemical environment. Several atomic and chemiluminescent spectra appear in the submicron range. A variety of particulate types glow as continuum blackbodies in the infrared. Subject to quantum mechanical restrictions, major and trace gases emit as well. Radio frequencies are attenuated by the weak plasma and may also be generated where charge separation and turbulence conjoin. Renewed interest in missile defense will motivate refinements in plume detection, particularly for the boost phase. We review current theory and modeling of exhaust chemistry in order to anticipate next-generation computations required to guide the sensor community. A variety of organic, composite, and liquid fuel types is described along with the dopants that can be introduced. Chemical behavior is outlined within thecombustion chamber and through the nozzle expansion zone. A brief history of exhaust kinetics modeling is then provided. Increasing complexity of reaction lists, integrators, and coupling to fluid dynamics are stressed. Parameterized submechanisms are recommended relevant to the major radiation interaction types. The nonequilibrium aerosol is dealt with over a range of compositions and sizes. We conclude by organizing a list of potential research priorities. Due to computational intensity and interdisciplinarity of the plume chemistry problem, cross-institutional programs are advised. Increased reaction detail should improve the performance of existing kinetics routines and lead also to convergence. Automation of chemistry setup and optimization of numerics will facilitate sensitivity tests and reaction tailoring. Multifluid hydrodynamics and gaseous electronic calculations may yield insights on radio frequency emissions from the backstreaming and Mach diamond regimes.