Fluctuations in glassy systems

We summarize a theoretical framework based on global time-reparametrization invariance that explains the origin of dynamic fluctuations in glassy systems. We introduce the main ideas without getting into much technical details. We describe a number of consequences arising from this scenario that can be tested numerically and experimentally, distinguishing those that can also be explained by other mechanisms from the ones that we believe are special to our proposal. We support our claims by presenting some numerical checks performed on the 3d Edwards-Anderson spin-glass. Finally, we discuss to what extent these ideas apply to super-cooled liquids that have been studied in much more detail to the present date.