  In the past 20 years, impressive progress has been made both experimentally
and theoretically in superconducting quantum circuits, which provide a platform
for manipulating microwave photons. This emerging field of superconducting
quantum microwave circuits has been driven by many new interesting phenomena in
microwave photonics and quantum information processing. For instance, the
interaction between superconducting quantum circuits and single microwave
photons can reach the regimes of strong, ultra-strong, and even deep-strong
coupling. Many higher-order effects, unusual and less familiar in traditional
cavity quantum electrodynamics with natural atoms, have been experimentally
observed, e.g., giant Kerr effects, multi-photon processes, and single-atom
induced bistability of microwave photons. These developments may lead to
improved understanding of the counterintuitive properties of quantum mechanics,
and speed up applications ranging from microwave photonics to superconducting
quantum information processing. In this article, we review experimental and
theoretical progress in microwave photonics with superconducting quantum
circuits. We hope that this global review can provide a useful roadmap for this
rapidly developing field.
