I will review the theory of the many-body localization phase transition and its implications for the dynamical phase structure of isolated interacting quantum systems, and the challenges and opportunities it presents in realizing and studying non-equilibrium phases of matter.

Refs: Ann. Physik 1600302 (2017); Phys. Rev. X 5, 031033 (2015); Phys. Rev. B 99, 094205 (2019); D.A. Abanin et al arXiv:1911.04501