In this talk, I will describe some general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries. Based only on representation theory, I will derive some general Mermin-Wagner-type principles governing the possible fates of non-equilibrium dynamics in isolated, disordered quantum systems. In particular, I will show that MBL cannot exist in the presence of non-Abelian symmetries. Consequences for the classification of MBL protected topological phases (and Floquet phases) will be discussed.