Synthetic gauge fields have many important physical consequences in quantum optical systems. This fast-growing topic of research is opening up new possibilities for the lossless optical transmission of information, for improved optical components, such as optical isolators, and even for fault-free topological quantum computing. We explore how to push cutting-edge experiments towards these goals by theoretically studying the interplay of synthetic gauge fields with optical nonlinearity, pumping and loss in photonic devices. The systems we shall investigate range from artificial graphene and other condensed matter models simulated with microcavities; to lattices of classical pendula and waveguides; to strongly correlated fractional quantum Hall-like states of light and their exotic excitations. Our work will have an immediate impact through international experimental collaborations and an interdisciplinary approach building on our combined range of expertise. We will exploit concepts and techniques from diverse research areas including quantum fluids, topological phases of matter, solid-state systems and non-equilibrium physics. Our project couples the investigation of novel phenomena arising from gauge fields in many-body systems with the hunt for new and improved technological applications in photonics.