Combustion is a complex phenomenon of interest that combines chemical reactions and turbulent flows. Resolution of both problems is a difficult task. On the one hand, chemical reactions introduce a large amount of species with different properties and small temporal scales due to chemical kinetics. On the other hand, turbulent flows imply a large span of spatial scales. Different models are commonly applied to reduce these requirements. Chemical reactions can be modeled with reduced chemical mechanisms. These have less species and reactions than complex ones, but are able to describe the combustion. Turbulence is modeled by means of Large Eddy Simulation (LES), which filters the Navier-Stokes equations spatially. Thus, the small scales of the flow are filtered out. These ones are modeled through a turbulent viscosity. The present study focuses on the theoretical basis required to model combustion phenomena. First, the algorithm used to solve variable density flows is presented. It uses the low-Mach equations, which are discretized in terms of the convective-diffusive equation. Its resolution is achieved by applying an algorithm based on a projection method, using a predictor-corrector step. Then the algorithm used to solve chemical kinetics is detailed. In this case, the Arrhenius law is used for laminar flames and a two equations model for turbulent flows. The latter introduces an eddy dissipation model besides the Arrhenius law to include the effect of the filtered spatial scales in LES simulations. The study concludes with an introduction to LES. The spatial filter introduces some additional terms in the governing equations. These ones are modeled through a turbulent viscosity. Different models to evaluate the turbulent viscosity can be found in the literature. In the present study the Smagorinsky model is used. Different tests are carried out to verify the results. The lid driven cavity and the heated cavity tests show that accurate results are obtained for incompressible and variable density non-reacting flows. A laminar methane/air flame test is used to verify the laminar chemical algorithm. Additionally, the influence of chemical mechanism on the flame behavior is shown. Finally, a three dimensional propane burner is simulated to study the turbulent combustion phenomena and verify the interaction between turbulent combustion chemical algorithm and LES. An additional test is used to assess the speedup of the parallelization implemented and also to check its performance.