Abstract: Classical general relativity describes the dynamics of gravity through the Einstein's equations, while relativistic fluids are governed by a generalization of the famous Navier-Stokes equations. Though a-priori we don't tend to think of these two physical systems in the same breath, I will argue that in a certain dynamical regime, the gravitational equations precisely become those of fluid dynamics. This statement, which embodies the fluid/gravity correspondence, has over the past few years not only helped us in understanding the transport properties of some strongly coupled systems, but is proving to be a prototype for the development of an autonomous theory of hydrodynamics. I will explain the basic statement of the correspondence and the lessons we have learned from it, focussing on the development of a Wilsonian effective field theory for thermal systems.
