This article begins with a synthetic presentation of key issues in the numerical description of combustion phenomena. Different levels of combustion modeling are identified and characterized. It is indicated how these modeling levels may be used to deal with fundamental questions or technological applications. Important advances have been made in detailed numerical modeling of complex flames and in direct simulation of flame/turbulence and flame/flow interactions. Results obtained in these areas have been employed to improve physical modeling methods which are currently used to calculate reactive flowfields in practical combustors operating in the turbulent regime. As physical modeling relies on average Navier-Stokes equations it requires closure rules for turbulent fluxes and for mean reaction rates. Considerable effort has been expanded to devise novel closure schemes or improve current models. Progress has been accomplished in the development of probabilistic methods in which the probability density function is calculated. Recent developments have concentrated on the incorporation of complex chemistry using various reduction schemes. Advances have also been made in descriptions based on flame surface density concepts. Transport equations for the flame surface have been refined by processing flame data bases generated by direct numerical simulations. Detailed experiments have also provided new insights on the fundamental mechanisms of turbulent combustion and observations have led to novel submodels. Another area of considerable interest for the future is that of large eddy simulation (LES). Progress accomplished in nonreactive LES provides a good starting basis but some challenging problems are encountered when dealing with combustion. The main difficulties are related to the determination of the position of the large scale flame on the coarse computational grid and to the definition of subgrid models for reaction in the small scales. Some novel schemes for combustion LES are reviewed and illustrated by typical examples of calculations