The Many-body localization (MBL) phenomenon is one the most extreme examples of ergodicity breaking at infinite temperature, thus challenging the very foundation of statistical quantum mechanics. The use of High-Performance (classical) Computers has been of great help to better understand how hot quantum matter behaves in the presence of strong randomness. Despite the long list of still open questions, we have been able to answer a few of them concerning MBL in quantum spin chains in a random magnetic field, a quite simple model which nevertheless contains extremely rich and non-trivial physics.