Anomalous Transport in Hydrodynamics and Gauge/Gravity Duality Out of Equilibrium

In this thesis we use the AdS/CFT correspondence to better understand the transport phenomena produced by the chiral anomaly. The main results of the thesis involve a study of anomalous transport from the perspective of the holographic renormalization group flow, an analysis of the effect that the inclusion of translation symmetry breaking can have on the anomalous transport coefficients, an exploration of the universality of a holographic model of Weyl semimetals and the algebraic structure of the anomaly, and, finally, the computation of the out of equilibrium response in the chiral magnetic effect. We perform theoretical work to grasp the subtleties of the mechanisms that produce these phenomena and try to give some hints for the phenomenology of the experimental systems in which these effects are relevant.