  We consider the current operators of one dimensional integrable models. These
operators describe the flow of the conserved charges of the models, and they
play a central role in Generalized Hydrodynamics. We present the key statements
about the mean currents in finite volume and in the thermodynamic limit, and we
review the various proofs of the exact formulas. We also present a few new
results in this review. New contributions include a computation of the currents
of the Heisenberg spin chains using the string hypothesis, and simplified
formulas in the thermodynamic limit. We also discuss implications of our
results for the asymptotic behaviour of dynamical correlation functions.
