The use of computational fluid dynamics (CFD) for the design and analysis of the flow and combustion in gas turbine combustors is considered to be a cost effective alternative to time-consuming and expensive design of experiments studies. With stringent emission regulations being enforced for these combustion systems, efforts towards optimization of the combustor geometry, and its operating conditions to minimize fuel consumption, emissions, and cost are also being undertaken using CFD. Reacting flow modeling in gas turbine combustors is a multi-scale, multi-physics process which requires an adequate representation of the flow, chemistry, and heat transfer mechanisms taking place in these systems. The models/approximations used in simulating gas turbine combustors directly influence the predictive capability of the simulations. In this study, the commercial software STAR-CCM+ is used model all the processes taking place in a gas turbine combustor. STAR-CCM+ solves the Navier-Stokes equation using the finite volume formulation. The choice to represent the combustion chemistry via global reactions, tabulated methodology, or detailed kinetic modeling is available for premixed, non-premixed and partially premixed combustion regimes. The combustion model selection is typically driven by the intended purpose of the simulation. Radiative heat transfer is modeled using the discrete ordinates methodology. In order to study the mechanical durability of various components in these systems, a full conjugate heat transfer (CHT) analysis is also performed where, the liner and other solids are explicitly modeled in the fully-coupled simulation. In this investigation, both the Reynolds Averaged Simulation (RANS) methodology and the Large-Eddy Simulation (LES) methodology are explored and the results are summarized.