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Abstract: Progress in the field of computational combustion over the past 50 years is reviewed. Particular attention is given to those classes of models that are common to most system modeling efforts, including fluid dynamics, chemical kinetics, liquid sprays, and turbulent flame models. The developments in combustion modeling are placed into the time-dependent context of the accompanying exponential growth in computer capabilities and Moore’s law. Superimposed on this steady growth, the occasional sudden advances in modeling capabilities are identified, and their impacts are discussed. Integration of submodels into system models for spark ignition, diesel and homogeneous charge, compression ignition engines, surface and catalytic combustion, pulse combustion, and detonations are described. Finally, the current state of combustion modeling is illustrated by descriptions of a very large jet lifted 3D turbulent hydrogen flame with direct numerical simulation and 3D large eddy simulations of practical gas burner combustion devices. [Copyright &y& Elsevier]