Microwave photonics with superconducting quantum circuits has advanced significantly in the past 20 years, offering new ways to manipulate microwave photons. This field combines superconducting quantum circuits with microwave photonics and quantum information processing, enabling strong, ultra-strong, and deep-strong coupling between superconducting circuits and single microwave photons. These interactions have led to the observation of phenomena such as giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments enhance understanding of quantum mechanics and accelerate applications in microwave photonics and quantum information processing. The review discusses experimental and theoretical progress in microwave photonics using superconducting quantum circuits. It covers basic concepts like qubits and resonators, various types of superconducting quantum circuits, and their interactions with microwave fields. The article also explores waveguide QED, quantum optics, and atomic physics on superconducting chips, including phenomena such as electromagnetically induced transparency, lasing, squeezed states, and photon blockade. It discusses nonlinear processes, photon generation and detection, and applications in quantum simulation and quantum information processing. The review highlights the unique properties of superconducting artificial atoms, which can be designed and controlled for various research purposes. These atoms can interact with microwave fields in ways that are not possible with natural atoms, enabling new quantum phenomena. The article also discusses the advantages and drawbacks of superconducting circuits compared to natural atoms, and provides a comprehensive overview of the field. It concludes with a summary and perspectives on the future of microwave photonics with superconducting circuits.Microwave photonics with superconducting quantum circuits has advanced significantly in the past 20 years, offering new ways to manipulate microwave photons. This field combines superconducting quantum circuits with microwave photonics and quantum information processing, enabling strong, ultra-strong, and deep-strong coupling between superconducting circuits and single microwave photons. These interactions have led to the observation of phenomena such as giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments enhance understanding of quantum mechanics and accelerate applications in microwave photonics and quantum information processing. The review discusses experimental and theoretical progress in microwave photonics using superconducting quantum circuits. It covers basic concepts like qubits and resonators, various types of superconducting quantum circuits, and their interactions with microwave fields. The article also explores waveguide QED, quantum optics, and atomic physics on superconducting chips, including phenomena such as electromagnetically induced transparency, lasing, squeezed states, and photon blockade. It discusses nonlinear processes, photon generation and detection, and applications in quantum simulation and quantum information processing. The review highlights the unique properties of superconducting artificial atoms, which can be designed and controlled for various research purposes. These atoms can interact with microwave fields in ways that are not possible with natural atoms, enabling new quantum phenomena. The article also discusses the advantages and drawbacks of superconducting circuits compared to natural atoms, and provides a comprehensive overview of the field. It concludes with a summary and perspectives on the future of microwave photonics with superconducting circuits.