How a closed quantum system reaches thermal equilibrium is a fundamental question in statistical physics. Recent work has uncovered surprising richness in this process, leading to a new classification of quantum many-body systems into distinct .dynamical phases.. On one extreme are many-body localized states, which fail to thermalize and can retain accessible quantum correlations indefinitely. At the other end are maximally chaotic systems, which scramble quantum information rapidly. I will review progress made in understanding many-body localized phases, both theoretically and experimentally. I will then discuss a novel approach for computing the time evolution of quantum many-body systems, which captures the emergence of chaos and hydrodynamic behavior.