Hydrodynamic instabilities produce material mixing that can significantly degrade weapons performance. We investigate the Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities in the turbulent regime in two experimental venues. RM experiments are conducted on the Nova laser with strong radiatively driven shocks (Mach > 20) in planar, two fluid targets. Interfacial perturbations are imposed with single sinusoidal modes to test linear theory and with three dimensional (3D) random modes to produce turbulent mix. RT experiments are conducted on a new facility, the Linear Electric Motor (LEM), in which macroscopic fluids are accelerated with arbitrary temporal profiles. This allows detailed diagnosis of the turbulence over a wide range of conditions. The Nova experiments study the high compression regime whereas the LEM experiments are incompressible. The results are compared to hydrodynamic simulations with the arbitrary Lagrangian-Eulerian code (CALE). The goal is to develop and test engineering models of mix.