Turbulent reacting flows with and without swirl are calculated using fast and finite-rate chemistry models and closure is effected by extending constant-density turbulence models to reacting flows. Three experimental combustor flow fields are compared with the calculations: one is a premixed, opposed-jet combustor and the other two are non-premixed, sudden-expansion combustors with and without swirl. The results indicate that an isotropic eddy viscosity model based on the turbulence kinetic energy (k) and its dissipation rate (ε) is sufficient to represent turbulence in non-swirling, reacting flows, whereas an algebraic stress model provides a better overall mean field prediction for reacting flows with swirl. However, flow expansion due to heat release during combustion is only fairly well represented by the submodels used. A finite-rate chemistry model is found to be superior to the fast chemistry approximation in the non-premixed combustor and a two-step global reaction mechanism gives an adequate description of flame stabilization in the premixed combustor. Unfortunately, neither model provides a realistic flame structure. Therefore. further development of finite-rate chemistry models with a suitable coupling of the heat release effects on the turbulence field are needed to improve reacting flow models.