We develop computational models for the numerical simulation of reacting flows in a wide range of combustion applications with a focus on laminar burners, gas-turbine combustors and heavy-duty engines. At the heart of our modeling research lies the FGM method, which has been invented by our group and is continuously further developed. Simulations employing detailed chemistry and transport models are used to investigate the structure, emissions, dynamics and stability of laminar flames. Our FGM model is extended to account for heat loss, fuel stratification, preferential diffusion, flame stretch/curvature effects, pollutant formation (UHC, CO, NOx, soot) and ignition/extinction. The interaction of flow and chemistry in turbulent flames is unraveled by using an in-house developed high-fidelity DNS code. Turbulent combustion models are developed and tested in an in-house LES code and validated against lab scale experiments. The knowledge from these studies is translated into efficient and accurate FGM-based models that are coupled to commercial and open-source CFD codes for the simulation of combustion in engineering applications.