Circuit QED is the application of the language and ideas of quantum optics and cavity QED to superconducting microwave circuits. Microwave resonators play the role of Fabry-Perot cavities and Josephson junction circuits (superconducting qubits) play the role of artificial atoms strongly coupled to microwave photons. The circuit QED architecture is the leading platform for creation of quantum computers based on superconducting circuits. In these lectures we explore current and future applications of this platform to the simulation of correlated quantum matter and lattice gauge theories. The native bosonic modes in this platform make it especially powerful for quantum simulation of physical models containing bosons.