The article "Many-Body Localization in the Age of Classical Computing" by Piotr Sierant et al. reviews the current understanding of many-body localization (MBL) in quantum systems. The authors provide a historical perspective on the development of MBL, from early studies of Anderson localization to the formulation of the eigenstate thermalization hypothesis (ETH) and the discovery of MBL. They define MBL as a phase of matter where thermalization does not occur, even in the asymptotic limit of infinite system size and evolution time. The review highlights the challenges in interpreting numerical results due to the exponential growth of the Hilbert space, which limits the accessible system sizes and time scales. The authors discuss various numerical methods used to study MBL, including exact diagonalization, time evolution methods, and tensor network approaches. They also explore the phenomenology of the ETH-MBL crossover, slow dynamics in disordered many-body systems, and the relationship between thermalization and transport. The review concludes by discussing extensions of MBL, experimental observations, and open questions in the field.The article "Many-Body Localization in the Age of Classical Computing" by Piotr Sierant et al. reviews the current understanding of many-body localization (MBL) in quantum systems. The authors provide a historical perspective on the development of MBL, from early studies of Anderson localization to the formulation of the eigenstate thermalization hypothesis (ETH) and the discovery of MBL. They define MBL as a phase of matter where thermalization does not occur, even in the asymptotic limit of infinite system size and evolution time. The review highlights the challenges in interpreting numerical results due to the exponential growth of the Hilbert space, which limits the accessible system sizes and time scales. The authors discuss various numerical methods used to study MBL, including exact diagonalization, time evolution methods, and tensor network approaches. They also explore the phenomenology of the ETH-MBL crossover, slow dynamics in disordered many-body systems, and the relationship between thermalization and transport. The review concludes by discussing extensions of MBL, experimental observations, and open questions in the field.