Superconducting circuits have emerged as a competitive platform for quantum computation, satisfying the challenges of controllability, long coherence and strong interactions. Here we apply this toolbox to a different problem: the exploration of strongly correlated quantum materials made of microwave photons. We develop a versatile recipe that uses engineered dissipation to stabilize many-body phases, protecting them against intrinsic photon losses in the circuits. We build a strongly interacting Bose-Hubbard lattice in superconducting circuits and applied our dissipative stabilization method to create a Mott insulator of photons. Site- and time-resolved microscopy of the lattice provides insights into the thermalization processes through the dynamics of defects in the Mott phase. In another experiment, we realize a superconducting Chern insulator constructed from tunnel-coupled, time-reversal broken microwave cavities and study its topologically protected edge states with time-resolved microscopy and momentum-resolved spectroscopy. With the introduction of qubit-mediated interactions, it would enable the exploration of strongly-correlated topological material in synthetic systems. Our experiments demonstrate the power of superconducting circuits for studying synthetic quantum matter in both coherent and engineered driven-dissipative settings. I will discuss some prospects including microscopic studies of strongly interacting topological phases and quantum thermodynamics.