Anomalies within magnetic holography Within gauge gravity duality we study the class of four dimensional CFTs with chiral anomaly described by Einstein Maxwell Chern Simons theory in five dimensions. In the first part of this thesis we compute quasinormal modes (QNMs) of the metric and gauge field perturbations about electrically and magnetically charged black branes. By the gauge gravity correspondence this theory is dual to a particular class of field theories with a chiral anomaly in a thermal charged plasma state subjected to a constant external magnetic field B. The QNMs are dual to the poles of the two point functions of the energy momentum tensor and axial current operators and they encode information about the dissipation and transport of charges in the plasma. Complementary to the gravity calculation we work out the hydrodynamic description of the dual field theory in the presence of a chiral anomaly and a constant external B. We find QNMs exhibiting Landau level behavior which become long lived at large B if the anomaly coefficient exceeds a critical magnitude. Chiral transport is analyzed beyond the hydrodynamic approximation for the five (formerly) hydrodynamic modes including a chiral magnetic wave. In the second part we consider the phase diagram at finite temperature chemical potential and magnetic field B. At high temperatures the solution is given by the electrically and magnetically charged AdS Reissner Nordstroem black brane studied in first part of this thesis. For sufficiently large Chern Simons coupling and at sufficiently low temperatures and small magnetic fields we find a new phase with helical order breaking translational invariance spontaneously. For the Chern Simons couplings studied the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.