A complete understanding of these fundamental instabilities is extremely challenging, given that the flows under consideration may include: multiple compressible species, shock waves, large variations in density, high geometrical convergence, and extremely small time scales. In laser-driven experiments, instability growth may be further modified by real gas effects, ablation, radiation, magnetic fields, conduction, viscous dissipation, and additional perturbation seeds such as drive nonuniformity. Experimentalists must develop innovative approaches to designing experiments with repeatable and characterizable flow conditions, incorporating advanced diagnostics which can extract quantitative, time-resolved data. Numericists must design robust numerical schemes capable of accurately simulating highly compressible, multispecies or multiphase flows with turbulent structures ranging in size from the mixing layer width to the Kolmogorov scale. Theoreticians must combine physical insight with experimental and numerical data to develop models which address the nonlinearities in the governing equations, or enable a reduction in problem dimensionality. These models may then predict the details of instability growth in new configurations or give insight into the fundamental physics of instability development. Despite these many challenges, great advances are being made in the understanding of these instability-driven turbulent flows. These advances are the focus of the International Workshop of the Physics of Compressible Turbulent Mixing (IWPCTM).