Recent progress on the phenomenon of many-body localization has revealed classes of generic (typically disordered) many-body systems which never reach local thermal equilibrium, and thus lie outside the framework of equilibrium statistical mechanics. MBL systems can undergo a dynamical phase transition to a thermalizing phase as parameters such as the disorder or interaction strength are tuned, and the nature of the MBL-to-thermal phase transition is an active area of research. The existence of MBL raises the interesting question of whether one can have different kinds of MBL phases, just as there are different kinds of thermalizing phases. Remarkably, the answer is affirmative, and out-of-equilibrium systems can also display a rich phase structure. What's more, the suppression of thermal fluctuations in localized systems can even allow for new kinds of order that are forbidden in equilibrium—which is the essence of localization-protected quantum order. The recent discovery of time-crystals in periodically driven MBL systems is a notable example of this phenomenon.