Abstract: I will review theoretical predictions and experiments showing that light propagating in a nonlinear optical medium can behave like a superfluid [1]. 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 other systems allowing for strong correlation between photons (such as superconducting quantum circuits), unconventional photon blockade effects with photonic dimers and new theory predictions for strongly correlated quantum phases in arrays of coupled cavities.