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Interacting artificial many-body systems play a fundamental role in the development of quantum simulators. Using engineered photonic systems, it has recently become possible to realize strongly interacting photon gases, which are particularly well suited for probing non-equilibrium many-body physics. The driven-dissipative nature of these systems is a major reason for the interest in them. Radiative losses are crucial to obtain real-time experimental access to the dynamical evolution of the quantum fluid, while new quantum phases of matter are expected to appear in such non-equilibrium many-body scenarios. These developments require novel theoretical tools to describe and understand them.