A few years after the first observation of Bose-Einstein condensation, quantum gases of photons in suitably designed photonic microstructures are establishing themselves as flexible and powerful platforms for the study of many-body physics in a completely novel context. In this talk, I will start by reviewing the first experiments that have demonstrated superfluid hydrodynamics effects in dilute photon fluids. When a localized defect is inserted in the flow, a wide range of behaviors have been observed depending on the flow speed, from superfluid flow to super-sonic Mach cones, to the nucleation of topological excitations such as solitons and vortices. I will then proceed with the presentation of more recent work on synthetical gauge fields for photons and, more generally, geometrical and topological effects in quantum fluids of light in the presence of periodic trapping potentials with different geometries. Perspectives towards the generation of strongly correlated photon gases in the presence of strong optical nonlinearities will be finally sketched, with a special attention to quantum Hall liquids of light and the detection of their exotic quasi-particle excitations.