Large-eddy simulation (LES) has traditionally been restricted to fairly simple geometries. This paper discusses LES of reacting flows in geometries as complex as commercial gas turbine engine combustors. The incompressible algorithm developed by Mahesh et al. (J. Comput. Phys., 2004, 197, 215-240) is extended to the zero Mach number equations with heat release. Chemical reactions are modeled using the flamelet/progress variable approach of Pierce and Moin (J. Fluid Mech., 2004, 504, 73-97). The simulations are validated against experiment for methane-air combustion in a coaxial geometry, and jet-A surrogate/air combustion in a gas-turbine combustor geometry.