  Holographic RG flows can be better understood with the help of radially
conserved charges. It was shown by various authors that the bulk gauge and
diffeomorphism symmetries lead to the conservation of the zero mode of the
holographic U(1) current and, if the spacetime is stationary, to that of the
holographic heat current. In describing dual theories with \'t Hooft anomalies
the bulk gauge invariance is broken by Chern-Simons terms. We show that
conservation laws can still be derived and used to characterize the anomalous
transport in terms of membrane currents at the horizon. We devote particular
attention to systems with gravitational anomalies. These are known to be
problematic due to their higher derivative content. We show that this feature
alters the construction of the membrane currents in a way which is deeply tied
with the anomalous gravitational transport.
