Lean premixed combustion (LPC) of natural gas is of considerable interest in land-based gas turbines for power generation. However, modeling such combustors and adequately addressing the concerns of LPC, which include emissions of nitrogen oxides, carbon monoxide and unburned hydrocarbons, remains a significant challenge. In this paper, characteristics of published simulations of gas turbine combustion are summarized and methods of modeling turbulent combustion are reviewed. The velocity-composition PDF method is selected for implementation in a new comprehensive model that uses an unstructured-grid flow solver. Reduced mechanisms for methane combustion are evaluated in a partially stirred reactor model. Comprehensive model predictions of swirl-stabilized LPC of natural gas are compared with detailed measurements obtained in a laboratory-scale combustor. The model is also applied to industrial combustor geometries.