An overview of theoretical and experimental work concerning the burning process in rocket propellant is presented. The current study has emphasized Ammonium Perchlorate (AP) / Hydroxyl Terminated Poly-Butadiance, (HTPB) composites rocket propellant. These propellants are widely used in a variety of rocket systems ranging from small tactical missiles to the large boosters that propel the space shuttle into orbit. A detailed review for the chemical kinetics, numerical and experimental models for the burning of the monomodal, bimodal, and multimodal propellants is introduced. Effects of propellant compositions, time-dependent pressure fluctuations, temperature, fuel-binder types, on the burning rate are reviewed and discussed. The result of the current study shows the effect of pressure and the AP particle sizes on the burning rate, the complex flame structure, and the morphology of the combustion surface.