Nanoscale electric and electronic circuits operate at low energy levels. In the RF regime, superconducting nanoelectronic devices exhibit tremendous potential since they allow for the generation, detection, mixing, and parametric amplification of RF signals. Modeling of such devices requires a treatment using quantum theory of circuits. Quantum effects can be exploited for RF microwave circuits, such as Josephson parametric amplifiers, in applications of quantum computing, communication, or sensing and imaging. We describe the modeling of microwave quantum circuits and their application to the example of quantum radar, where they provide for squeezed state generation and mixing.