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This document discusses results concerning mathematical theory, computational methods, and statistical modeling of chaotic mixing processes. In mathematical theory, the authors have proposed a new paradigm from uniqueness and regularization of discontinuous solutions of hyperbolic conservation laws. Contrary to common opinion, there is no requirement from physics for uniqueness of solutions for these systems. Nonuniqueness, if it occurs, must be resolved as in bifurcation theory by an unfolding of critical bifurcation parameters. Similarly regularization does not have to be accomplished by higher order terms in an equation, but may be based on enlarging the system. Many common mathematically based entropy conditions have been shown to be inadequate in specific examples. Work is in progress on two dimensional nonlinear wave interactions, from a theoretical point of view. Computationally, several difficult phenomena were encountered in the study of shock waves interacting with a liquid-gas interface. Chaotic mixing due to a Rayleigh-Taylor or Richtmyer-Meshkov unstable interface has been studied. Front tracking has provided a unique computational tool, and has produced a unique data set of computational results which are presently being analyzed. High quality models for single-mode growth in the large amplitude regime have been proposed, and validated.