Computer modeling of low-emissions gas-turbine combustors requires inclusion of finite-rate chemistry and its interactions with turbulence. The purpose of this review is to outline some recent developments in and applications of the physical models of combusting flows. The models reviewed included the sophisticated and computationally intensive velocity-composition pdf transport method, with applications shown for both a laboratory flame and for a practical gas-turbine combustor, as well as a new and computationally fast PSR-microstructure-based method, with applications shown for both premixed and nonpremixed flames. Calculations are compared with laser-based spectroscopic data where available. The review concentrates on natural-gas-fueled machines, and liquid-fueled machines operating at high power, such that spray vaporization effects can be neglected. Radiation and heal transfer is also outside the scope of this review.