<i>Colloquium</i>: Many-body localization, thermalization, and entanglement

The route of a physical system toward equilibrium and thermalization has been the subject of discussion and controversy since the time of Boltzmann. This Colloquium reviews the recent progress in understanding many-body localization, a phase of matter in which quantum mechanics and disorder conspire to prohibit thermalization altogether. Many new phenomena emerge in lieu of conventional statistical mechanics and may be observed in systems of ultracold atoms, superconducting qubits, and certain quantum materials.