Hypersonic flight and propulsion pose fundamental challenges that arise from interactions between shock waves and turbulence. These interactions can be beneficial, enhancing the mixing of fuel and oxidizer in a scramjet engine, but they can also be detrimental, compromising the integrity of the flying vehicle through uncontrolled aerothermostructural coupling. This presentation will highlight recent developments on the prediction and understanding of these phenomena by means of high-fidelity numerical simulations. First, focus will be placed on interactions of shock waves reflecting off turbulent boundary layers that develop along rigid and flexible walls, by loosely coupling a wall-modeled large-eddy simulation solver for the fluid flow with an elastic solid structural solver that accounts for geometric nonlinearities. Strong shock/boundary-layer interactions will be emphasized, resulting in mean flow separation and low-frequency unsteadiness that can couple with natural frequencies of the solid structure. Simulation results will be compared with supersonic wind-tunnel experiments. Second, the enhancement of scalar mixing under canonical shock-turbulence interactions will be addressed by means of shock-capturing direct numerical simulations, evaluating the effects of the shock and turbulence Mach numbers, and the Reynolds number. Statistical analyses will highlight changes along the mean flow direction of scalar variance and dissipation-rate budgets, flow topology, and alignments of the scalar gradient with vorticity and strain-rate eigendirections. A novel methodology to track the time evolution of geometric and physical quantities of turbulent flow structures will be introduced and applied to study the dynamics of isoscalar surfaces across the shock-turbulence interaction.