Title: Strongly correlated photons in coupled cavity/circuit QED systems Abstract: Motivated by the recent success of engineering strong light-matter interaction in various cavity/circuit QED architectures, there has been a surge of interest in realizing condensed matter-like systems with photonic systems. One of the most exciting questions in this emerging field is whether one can realize a superfluid-Mott insulator (SF-MI) transition of strongly correlated polaritons. The Jaynes-Cummings-Hubbard Model (JCHM) has been introduced to describe such a quantum phase transition of light in an array of coupled QED cavities, each containing a single photonic mode interacting with a two-level system. In the first part of this talk we review recent theoretical results on the phase diagram, excitations and critical exponents of the JCHM and discuss similarities and differences with the seminal Bose-Hubbard model (BHM) describing ultra-cold atoms in optical lattices. In the second part of the talk, we show that even in the simplest case of two coupled cavities (Jaynes-Cummings dimer) a sharp non-equilibrium self-trapping transition exists, which is reminiscent of the equilibrium SF-MI transition in an infinite array. We show that the proposed system is realizable with the current generation of circuit-QED technology. Additionally, we point out a number of novel and interesting features due the dissipative nature of the circuit QED realization.