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I will review theory and experiments showing that light propagating in a nonlinear optical medium can behave like a superfluid. The nonlinear medium of choice is a semiconductor in which photons hybridize with optical excitations of the material, or excitons. The hybrid quanta, polaritons, behave like particles forming a superfluid. It has a rich phenomenology, which includes hydrodynamical formation of vortices and dark solitons, and emission of "supersonic Cherenkov radiation" when hitting an obstacle. I will also discuss promising systems allowing for strongly correlated photon phases in arrays of nonlinear cavities and exciting new theory predictions of unconventional photon blockade effects.