Predictive modelling of turbulent combustion is important for the development of airbreathing engines, internal combustion engines, furnaces and for power generation. Significant advances in modelling non-reactive turbulent flows are now possible with the development of large eddy simulation (LES), in which the large energetic scales of the flow are resolved on the grid while modelling the effects of the small scales. Here, we discuss the use of combustion LES in predictive modelling of propulsion applications such as gas turbine, ramjet and scramjet engines. The LES models used are described in some detail and are validated against laboratory data-of which results from two cases are presented. These validated LES models are then applied to an annular multi-burner gas turbine combustor and a simplified scramjet combustor, for which some additional experimental data are available. For these cases, good agreement with the available reference data is obtained, and the LES predictions are used to elucidate the flow physics in such devices to further enhance our knowledge of these propulsion systems. Particular attention is focused on the influence of the combustion chemistry, turbulence-chemistry interaction, selfignition, flame holding burner-to-burner interactions and combustion oscillations.