Advances in computing power have enabled opportunities for computational modeling and simulation to enhance our understanding of fluid mixing and combustion in aerospace applications operating at extreme conditions. Large eddy simulation (LES) is a powerful technique for research into turbulent flows that offers a favorable balance between high-fidelity and computational feasibility. While the LES technique has been well-developed primarily in the context of low-pressure flows, its extension and application to complex, multi-physics flows has remained questionable. The strongly coupled non-linear physics of the governing multi-scale, physico-chemical processes in high-pressure turbulent combustion result in severe limitations and uncertainties in the application of LES to systems of practical interest. The scope of this research is to investigate the theoretical and modeling framework for LES of multi-scalar turbulent mixing and combustion at supercritical pressures encountered in liquid rocket engines and to establish a consistent and accurate approach for modeling necessary physics.