The semiclassical description of CFT in the large charge regime

I will give an overview of the progress made in recent years in the study of CFT data for large charge operators using the semiclassical approximation. The basic result is that, in this regime, the data are universally codified by the dynamics of a superfluid phase for the theory compactified on the cylinder. The advances so far mostly concerned euclidean correlators, but I will describe a first set of results for the correlators of charge and energy flux in lorentzian signature.