The paper reviews recent developments in the statistical mechanics of isolated quantum systems, focusing on the concepts of quantum thermalization and many-body localization (MBL). Quantum thermalization refers to the process where a closed quantum system, initially prepared in a non-equilibrium state, evolves to a state that is statistically indistinguishable from a thermal equilibrium state. This process is governed by the Eigenstate Thermalization Hypothesis (ETH), which posits that all many-body eigenstates of a Hamiltonian obey the laws of thermal equilibrium. However, not all systems thermalize; many-body localized systems, where the long-time properties are not captured by conventional ensembles of quantum statistical mechanics, are of particular interest. These systems can locally remember information about their initial conditions for arbitrarily long times, making them potential candidates for quantum information storage. The paper discusses the key features of MBL, including the existence of a quantum phase transition between the thermal and MBL phases. This transition is visible through the properties of single-eigenstate ensembles, which reveal ordered phases and phase transitions that are invisible to equilibrium statistical mechanics. The review also explores the phenomenology of MBL, such as the violation of ETH, the presence of a many-body mobility edge, and the behavior of entanglement and local spectra in these systems. The authors emphasize that while MBL systems do not thermalize, they exhibit rich and complex dynamics, including the possibility of ordered phases and phase transitions at high energies and low spatial dimensions, where equilibrium ordering is forbidden. The review concludes by highlighting open questions and future directions in the study of MBL, including the nature of the many-body localization phase transition and the role of quasiperiodic systems in supporting localization.The paper reviews recent developments in the statistical mechanics of isolated quantum systems, focusing on the concepts of quantum thermalization and many-body localization (MBL). Quantum thermalization refers to the process where a closed quantum system, initially prepared in a non-equilibrium state, evolves to a state that is statistically indistinguishable from a thermal equilibrium state. This process is governed by the Eigenstate Thermalization Hypothesis (ETH), which posits that all many-body eigenstates of a Hamiltonian obey the laws of thermal equilibrium. However, not all systems thermalize; many-body localized systems, where the long-time properties are not captured by conventional ensembles of quantum statistical mechanics, are of particular interest. These systems can locally remember information about their initial conditions for arbitrarily long times, making them potential candidates for quantum information storage. The paper discusses the key features of MBL, including the existence of a quantum phase transition between the thermal and MBL phases. This transition is visible through the properties of single-eigenstate ensembles, which reveal ordered phases and phase transitions that are invisible to equilibrium statistical mechanics. The review also explores the phenomenology of MBL, such as the violation of ETH, the presence of a many-body mobility edge, and the behavior of entanglement and local spectra in these systems. The authors emphasize that while MBL systems do not thermalize, they exhibit rich and complex dynamics, including the possibility of ordered phases and phase transitions at high energies and low spatial dimensions, where equilibrium ordering is forbidden. The review concludes by highlighting open questions and future directions in the study of MBL, including the nature of the many-body localization phase transition and the role of quasiperiodic systems in supporting localization.