Chiral fluids: a few theoretical issues

We review briefly a few topic concerning physics of fluids whose constituents are massless fermions interacting in chiral invariant way. Macroscopic manifestations of the chral anomaly is one of central issues. Another topic is ultraviolet vs infrared sensistivity of chiral magnetic and vortical effects. To clarify dynamical issues involved we rely mostly on a (well-known) toy model of pionic superfluidity.