This article reviews recent theoretical and experimental advances in understanding and controlling quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with novel features stemming from its non-equilibrium nature. The review covers a wide range of photon hydrodynamical effects, including superfluid flow around defects at low speeds, the appearance of a Mach-Cherenkov cone in supersonic flow, and the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the focus is primarily on planar semiconductor microcavities in the strong light-matter coupling regime, the concept of quantum fluids of light applies to a broader spectrum of systems, including bulk nonlinear crystals, atomic clouds in optical fibers and cavities, photonic crystal cavities, and superconducting quantum circuits based on Josephson junctions. The article concludes with a discussion on the exciting perspectives for achieving strongly correlated photon gases, including mechanisms for efficient photon blockade, novel quantum phases in arrays of strongly nonlinear cavities, and the rich phenomenology offered by artificial gauge fields for photons.This article reviews recent theoretical and experimental advances in understanding and controlling quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with novel features stemming from its non-equilibrium nature. The review covers a wide range of photon hydrodynamical effects, including superfluid flow around defects at low speeds, the appearance of a Mach-Cherenkov cone in supersonic flow, and the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the focus is primarily on planar semiconductor microcavities in the strong light-matter coupling regime, the concept of quantum fluids of light applies to a broader spectrum of systems, including bulk nonlinear crystals, atomic clouds in optical fibers and cavities, photonic crystal cavities, and superconducting quantum circuits based on Josephson junctions. The article concludes with a discussion on the exciting perspectives for achieving strongly correlated photon gases, including mechanisms for efficient photon blockade, novel quantum phases in arrays of strongly nonlinear cavities, and the rich phenomenology offered by artificial gauge fields for photons.