Quantum coherence and criticality at infinite temperature

Interacting many-body quantum systems often exhibit chaotic dynamics that rapidly ``scramble'' quantum information and lead to highly entangled states whose local properties are thermal and classical. A dramatic exception occurs in isolated and disordered systems where thermalization can be prevented by many-body localization, resulting in quantum coherent dynamics at high energy density. In this talk, I will discuss the new types of non-equilibrium phases and phase transitions that can arise in such systems, with an emphasis on the emergence of universality far from thermal equilibrium.