Shock-driven multiphase flows are fundamental to many emerging technologies such as scramjet engines, rotating detonation engines, selectively sensitive explosives, ultrasound-based treatment procedures, and additive manufacturing techniques to name a few. It is important to understand the interfacial dynamics in these multiphase systems to design and predict their behavior. Computational methods provide a less expensive route to study the interfacial dynamics in multiphase systems with the advantage of high spatiotemporal resolution compared to experimental methods. My research interests lie in developing high-resolution computational models to study the dynamic behavior of multiphase systems at the length scale of the interfaces. In this chapter, I shall demonstrate a Cartesian grid-based sharp-interface approach for modeling high-speed multiphase–multimaterial flows. The interfaces are tracked sharply using the levelset method. Numerical methods are developed to accurately couple the flow fields of the phases separated by the sharp interface embedded in the Cartesian grid. Adaptive mesh refinement is used to maintain a high resolution at a tractable computational cost. I shall discuss our recent findings from the high-resolution computational models of shock-induced combustion of aluminum droplets, ignition of composite explosives, and ultrasound-driven cavitation in soft tissues developed using this approach. Furthermore, such computational methods can be used to develop surrogate models of complex multiphase systems from ensembles of interface-resolved simulations. These surrogates constructed from direct numerical simulations of multiphase flows at the micro/mesoscale can be potentially used as high-fidelity sub-grid-scale models in predictive process-scale simulations of rocket engines, scramjet engines, and the detonation of explosive devices in the future.