With the advent of new experimental devices in the last decade, nonlinear quantum dynamics has been studied in a variety of realizations in atomic, molecular and condensed matter physics. In particular, superconducting circuits, originally designed as promising resources for quantum information processing, provide means to access nonlinear dynamics under well-controlled conditions from the classical down to the deep quantum regime. Very recently, in an extension of circuit quantum electrodynamics, quantum electronics has been combined with photonics to the new field of Josephson photonics, where the interaction of charge quanta with photons gives rise to a wealth of phenomena. Theory is thus challenged to capture nonlinear resonances far from equilibrium, non-classical states of light, photon entanglement and various quantum-classical crossovers. In this talk I will discuss the background, specific examples and future perspectives.