Three general classes of models that describe the processes occurring in diabatic flow in ducts having supersonic entry conditions are discussed. They are: integral techniques, finite-difference methods, and exact two-dimensional planar flame models formulated on the basis of instantaneous heat release. All three methods rigorously satisfy the conservation equations. The first two methods provide a basis for predicting and analyzing supersonic combustor performance. The careful interpretation and judicious use of experimental observations are crucial for the successful application of these methods. Comparisons of analytical and experimental results are presented, and generalized parametric studies are included. The third method is based on an idealized mixing and combustion model that may not be achievable, but nonetheless serves as a valuable analytical tool for explaining complex processes involving shock waves and heat addition. Results from four types of flow structures are discussed. Nomenclature A = cross-sectional area Af = projected area of inlet Aw = wall area