A generic formulation for modeling the sub-grid combustion in compressible, high Reynolds number, two-phase, reacting flows has been developed and validated. A sub-grid mixing/combustion model called Linear Eddy Mixing (LEM) model has been extended to compressible flows and used inside the framework of Large Eddy Simulation (LES) in this LES-LEM approach. The LES-LEM approach is based on the proposition that the basic mechanistic distinction between the convective and the molecular effects should be preserved for accurate prediction of the complex flow-fields such as those encountered in many combustion systems. In LES-LEM, all the physical processes such as molecular diffusion, small and large scale turbulent convection and chemical reaction are modeled separately but concurrently at their respective time scales. This multi-scale phenomena is solved using a two-scale numerical approach, wherein molecular diffusion, small scale turbulent convection and chemical reaction are grouped as small scale processes and the convection at the (LES grid) resolved scales are deemed as the large scale processes. Small-scale processes are solved using a hybrid finite-difference Monte-carlo type approach in a one-dimensional domain. Large-scale advection on the three-dimensional LES grid is modeled in a Lagrangian manner that conserves mass. Liquid droplets (represented by computational parcels) are tracked using the Lagrangian approach wherein the Newton's equation of motion for the discrete particles are integrated explicitly in the Eulerian gas field. Drag effects due to the droplets on the gas phase and the heat transfer between the gas and the liquid phase are explicitly included. Thus, full coupling is achieved between the two phases in the simulation. Validation of the compressible LES-LEM approach is conducted by simulating the flow-field in an operational General Electric Power Systems' combustor (LM6000). The results predicted using the proposed approach compares well with the experiments and a conventional (G-equation) thin-flame model. Particle tracking algorithms used in the present study are validated by simulating droplet laden temporal mixing layers. Comparison of the energy growth in the fundamental and sub-harmonic mode in the presence and absence of the droplets shows excellent agreement with spectral DNS. Finally, to test the ability of the present two-phase LES-LEM in simulating partially premixed combustion, a LES of freely propagating partially premixed flame in a droplet-laden isotropic turbulent field is conducted. LES-LEM along with the spray models correctly captures the flame structure in the partially premixed flames. It was found that most of the fuel droplets completely vaporize before reaching the flame, and hence provides a continuous supply of reactants, which results in an intense reaction zone similar to a premixed flame. Some of the droplets that did not evaporate completely, traverse through the flame and vaporize suddenly in the post flame zone. Due to the strong spatial variation of equivalence ratio a broad flame similar to a premixed flame is realized. Triple flame structure are also observed in the flow-field due to the equivalence ratio fluctuations.