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Tremendous progress has been achieved in the last ten years with respect to modeling the combustion of solid propellants. The vastly increased performance of computing capabilities has allowed utilization of calculation approaches that were previously only conceptual. The paper will discuss three areas of emphasis: first, numerical modeling of premixed flames using detailed kinetic mechanisms; second, development of packing models to calculate a geometrical distribution of particles simulating a heterogeneous solid propellant; and finally, calculation of diffusion same effects that are critical in the combustion of AP/hydrocarbon solid propellants. The capability of modeling premixed combustion using detailed kinetic mechanisms has been evolving and successfully applied to solid propellant ingredients based on a one-dimensional approach. Much of the early work was performed at Novosibirsk. The approach allows calculating the burning rate as a function of pressure but also the temperature sensitivity and spatial distributions of temperature and species concentrations. Generalized mechanisms have been developed and applied to many ingredients such as HMX, GAP, RDX, NG, AP, etc. The gas-phase kinetic mechanisms seem to represent the chemistry of these monopropellants and pseudo-propellants consistently well. The burning rates of these monopropellants vary by almost an order of magnitude but are essentially independent of the flame temperature. Various model calculations agree reasonably well with available experimental data. Recent work in the USA has been aimed at describing the geometrical packing of a solid propellant. These models represent significant progress toward such a description. Combining the packing model with a realistic flame model is still a significant challenge. Preliminary results are encouraging, but obviously further work is needed. Also, fundamental calculation of two-dimensional diffusion flames, incorporating realistic kinetics has progressed significantly. Recent results show encouraging promise toward simulating the minute detail involved in determining the burning rates of AP containing propellants. [ABSTRACT FROM AUTHOR]