Absract 

Typical quantum systems prepared in an out-of-equilibrium state will quickly approach a state of thermal equilibrium, even when there is no coupling to an external thermal bath. The approach to equilibrium is governed by a classical hydrodynamics of diffusing charges without significant quantum effects. A growing number of new scenarios that escape this classical description and remain out of equilibrium forever (or for parametrically long times) have been discovered, and are newly accessible to coherent quantum experiments. In certain 1D systems, closeness to an "integrable point" with an extensive number of extra symmetries delays equilibrium, and hydrodynamics is substituted by a strange hydrodynamic-like theory with many anomalous effects. In systems with strong disorder, localization completely kills transport altogether. I will describe our efforts to understand the dynamics in these new phases.