  Chiral anomalies have profound impact on the transport properties of
relativistic fluids. In four dimensions there are different types of anomalies,
pure gauge and mixed gauge-gravitational anomalies. They give rise to two new
non-dissipative transport coefficients, the chiral magnetic conductivity and
the chiral vortical conductivity. They can be calculated from the microscopic
degrees of freedom with the help of Kubo formulae. We review the calculation of
the anomalous transport coefficients via Kubo formulae with a particular
emphasis on the contribution of the mixed gauge-gravitational anomaly.
