Systems in cavity or circuit QED (Quantum Electrodynamics) are extensively studied in the context of quantum information and quantum computing. In addition, studying the non-equilibrium dynamics of photons in these open quantum systems is a challenging theoretical question. Studying “versatile lattice versions of these systems”  open new doors to quantum simulation, similar to ultra-cold atoms in optical lattices. In this Talk, we review our recent theoretical progress regarding (i) the development of methods to address the dynamics of driven and dissipative light-matter systems beyond the weak-coupling limit and (ii) the realization of topological phases of light in superconducting QED-circuit arrays through synthetic gauge fields. Effects of disorder will be studied. We also comment on the current experimental status in circuit QED systems.