High-speed particle-laden flows are studied through a combination of high-order Eulerian Lagrangian (EL) method development, multi-scale modeling and the analysis of normal, shear and wake instabilities. The EL code is based on a Weighted Essentially Non-Oscillatory (WENO) discretization, which captures discontinuities sharply while ensuring higher-order resolution in smoother areas. The favorable characteristics of WENO methods are extended to the EL framework with an Essentially Non-Oscillatory (ENO) scheme to interpolate the carrier phase from the Eulerian grid to the particle location. A high fidelity multi-scale method is introduced that couples full-resolution microscale statistics with the macro-scale. Using a Taylor expansion of the drag correction factor and Reynolds averaging of the particle transport equation, the Subgrid Particle Reynolds Stress Equivalent (SPARSE) model is derived. A mantle is constructed to provide closure for the particle drag and subgrid particle dynamics models. The efficacy of several metamodeling techniques in building a mantle with a target uncertainty using the least number of support points is compared. Grid aligned shocks at high mach numbers create normal instabilities that bleed into the particle phase. These so-called "carbuncles" have a predominantly numerical nature and can be mitigated by adjusting the nonlinear WENO power parameters. Instabilities that are induced by the accelerated flow behind a moving shock in the wake of a cloud of particles are analyzed. The initial shape, orientation and dimensionality of the particle cloud with respect to an oncoming normal shock determines the particle dispersion at later times. Dispersion characteristics are matched with results reported in literature. Streamlined cloud shapes exhibit a lower dispersion as compared to clouds with an initially blunt shape. Lower particle number density areas away from the heavily populated cloud core accelerate more. Growth rates of shear instabilities computed with the EL code are compared with the results of a linear stability analysis of particle-laden shear layers. The growth rate of shear layers with non-uniformly laden low Stokes number particles is greater than an unladen shear layer whereas a shear layer with high Stokes number particles dampens the growth.