Consider a generic interacting system of infinitely many degrees of freedom, interacting internally but isolated from any other systems. In standard statistical mechanics we assume that this system’s dynamics will approach thermal equilibrium in the limit of long time. This is what is now termed “thermalization”. I will discuss some aspects of thermalization, particularly for quantum many-body systems. The idea that some such quantum many-body systems do not thermalize and instead remain many-body localized (MBL) in a state that is in some sense near to the initial state was the motivation of Anderson’s original 1958 paper introducing the concept of Anderson localization. I will discuss some aspects of the present understanding of many-body localization, and the novel dynamical quantum phase transition between MBL and thermalization.