Turbulent spray combustion is an industrially relevant flow found in aircraft engines, stationary turbines, diesel and spark ignition engines, industrial furnaces, and chemical reactors. In these flows, a liquid reactant in the form of droplets is dispersed in a turbulent carrier-gas flow. Spray flames exhibit complex morpholgies and contain premixed, non-premixed, and partially-premixed propagation mechanisms. A predictive model for this challenging system will have direct impact in a wide range of industries. The objective of this work is to develop a state-of-the-art two-phase filtered-density function approach for turbulent spray combustion. The entire formulation is based on the large-eddy simulation methodology that captures large-scale mixing accurately. This formulation has multiple advantages. First, the chemical source term in the gas-phase appears requires no modeling. Second, detailed models for the turbulent spray dispersion process can be formulated. Third, nonequilibrium sub-filter models for the gas-phase turbulent flux can be specified. We demonstrate that without addressing these issues, a predictive model for turbulent spray combustion cannot be formulated. DNS computations are used to test the sub-filter closures developed. Further, a unique detailed computational method is formulated for understanding the flame propagation in a representative droplet group is presented.