Chiral anomalies have profound impact on the transport properties of relativistic fluids. They are closely related to the creation of currents by magnetic fields or vortices in the fluid via the so called Chiral Magnetic Conductivity and the Chiral Vortical Conductivity. Both can be computed by Kubo type formulae from special kinematic limits of two point functions of currents. I will review the calculation of these conductivites in a gas of free Weyl fermions and at strong coupling via a holographic model. A special and somewhat mysterious role is played by the mixed gauge-gravitational anomaly.