Turbulent swirling flows and methane-air swirling diffusion combustion are simulated by both large-eddy simulation (LES) using a Smagorinsky-Lilly subgrid-scale (SGS) turbulence model, a second-order moment (SOM) subgrid-scale combustion model and an eddy break up (EBL) combustion model and Reynolds-averaged Navier-Stokes (RANS) modeling using the Reynolds stress equation model and a second-order moment (SOM) combustion model. For swirling flows, the LES statistical results give better agreement with the experimental results than the RANS modeling, indicating that the adopted subgrid-scale turbulence model is suitable for swirling flows. For swirling combustion, both the proposed SOM SGS combustion model and the RANS-SOM model give the results in good agreement with the experimental results, but the LES-EBU modeling results are not in agreement with the experimental results.