Analogue Models of Gravity: The ubiquitous space-time

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Analogies have played a very important role in physics and mathematics, as they provide new ways of looking at problems that permit cross-fertilization of ideas among different branches of science. An analogue gravity model is a generic dynamical system (typically but not always based on condensed matter physics) where the propagation of excitations/perturbations can be described via hyperbolic equations of motion possibly characterized be one single metric element for all the perturbations. We shall review the historical development of this field, some of the systems proposed, and discuss several applications of this fruitful analogy mainly in the context of black hole physics and cosmology. While typical applications are in the realm of classical and quantum field theory on curved spacetime, I shall in the end also discuss recent developments which may provide insights about the possible nature of gravitational dynamics in emergent gravity scenarios.