  Generalized Hydrodynamics is a recent theory that describes the large scale
transport properties of one dimensional integrable models. At the heart of this
theory lies an exact quantum-classical correspondence, which states that the
flows of the conserved quantities are essentially quasi-classical even in the
interacting quantum many body models. We provide the algebraic background to
this observation, by embedding the current operators of the integrable spin
chains into the canonical framework of Yang-Baxter integrability. Our
construction can be applied in a large variety of models including the XXZ spin
chains, the Hubbard model, and even in models lacking particle conservation
such as the XYZ chain. Regarding the XXZ chain we present a simplified proof of
the recent exact results for the current mean values, and explain how their
quasi-classical nature emerges from the exact computations.
