Interface and mixing and their non-equilibrium kinetics and dynamics couple micro to macro scales, and are ubiquitous to occur in fluids, plasmas and materials, in high energy density regimes. Stellar evolution, plasma fusion, reactive fluids, purification of water, and nanofabrication are a few examples of many processes to which dynamics of interfaces is directly relevant. This talk presents the rigorous theory of the stability of the interface – a phase boundary broadly defined. We directly link the structure of macroscopic flow fields to microscopic interfacial transport, quantify the contributions of macro and micro stabilization mechanisms to interface stability, and discover the fluid instabilities never previously discussed. In ideal and realistic fluids, the interface stability is set primarily by the interplay of the macroscopic inertial mechanism balancing the destabilizing acceleration, whereas microscopic thermodynamics create vortical fields in the bulk. By linking micro to macro scales, the interface is the place where balances are achieved.