The holographic correspondence is a map between quantum field theories and higher dimensional theories of gravity. With historical roots in the seventies, when remarkable discoveries about black hole entropy and large N gauge theories were made, it found its first concrete realization in the late nineties, in the context of string theory. A relevant aspect of the correspondence is that it works as a duality: it maps non-perturbative regimes on one side into perturbative regimes in the other. This offers, in principle, the opportunity to shed new light on the physics of quantum systems which evade standard descriptions based on weakly interacting quasi-particles, by means of simple classical gravity methods. Despite the fact that the models we can precisely access with these methods are still quite far from realistic quantum field theories, there are relevant cases in which this limitation appears to be less severe. In those cases, holography has provided novel effective descriptions and a set of unique benchmark results for phenomenologically relevant systems. Concrete applications to the quark-gluon plasma phase of QCD, the strange metal phase of quantum critical systems in condensed matter and entanglement physics, will be discussed.
