Where we see how deep was the insight of Gibbs, Duhem, and Hugoniot when they imagined the propagation of large classes of mobile thin zones of rapidly varying fields, and how the Maxwell-Hadamard vision of discontinuity surfaces and Eshelby’s ideas of driving force fit in their pioneering views and allow now for a satisfactory approach, analytical and numerical, to the propagation of many physical phenomena involving evolving transition zones, in particular shock waves, phase-transition fronts, and grain boundaries.