A methodology for computing steady turbulent combusting flow in combustors of complex shape is presented. Included is discussion of fully- or partially-equilibrated chemical kinetic models, the interaction of turbulence and combustion, grid systems, discretization operators and solution procedures for recirculating flows. Examples that demonstrate the influence of these issues are reviewed. A package of three-dimensional codes for grid generation and flow analysis-developed in the course of these studies-is applied to the flow in a sector of a modern annular gas-turbine combustor. Results are compared with available data. The study demonstrates the utility of modern computational methods and indicates directions for future work