In the physics of strongly correlated quantum systems the electromagnetic radiation has traditionally assumed the role of a spectroscopic probe and thus treated as a classical field. In recent years an increasing control over light-matter interactions at the genuine quantum level has been achieved due to experimental developments in quantum optics and quantum electronics. This has brought forth a novel class of many body systems where elementary excitations are made by single quanta of light and matter. These hybrid setups are currently attracting a great experimental and theoretical interest, for the unique features they offer to explore quantum many body physics in novel far from equilibrium regimes. Motivated by the experimental effort, currently ongoing at Princeton, to realize these correlated systems of photons and atoms using superconducting circuits, in this talk I will discuss the physics of large arrays of microwave resonators coupled to superconducting qubits via the elementary Rabi non-linearity. I will argue that the very nature of photon field and its interaction with matter-like excitations allows to stabilize finite-density quantum phases of correlated photons out of the vacuum. I will discuss the properties of these phases and the quantum phase transition occurring between them and highlight the differences with the physics of interacting massive quantum particles.