Quantum microwave has both the quantum characteristics of the quantum signal and the ability of long-distance propagation in free space. It has extensive applications in various fields, such as communication, radar, navigation and positioning. This article summarized and analyzed the characteristics of quantum microwave and its receiving methods in light of the relatively less research on the reception of quantum microwave at present. We started from introducing the characteristics and preparation methods of single microwave photon, entangled microwave photon pairs, and squeezed state or entangled state microwave fields. We then introduced the receiving principle and detection methods of quantum microwave, and particularly paid intensive attention on the current status and existing problems in both the quantum radar and other physical systems. The main problems include: the signal strength is rather weak at the receiver; the detection technique for the microwave entangled state is not mature enough; and the optimal detection operator is to be further optimized, etc. For this, we summarized and analyzed the potential strategies of lowering down the noise in the receiver to improve the signal to noise ratio, and the path entanglement microwave detection approach based on the entanglement witness. Thus, a closed path is completed starting from the preparation and generation until the receiving of the quantum microwave. We hope that this review can provide some support for the development of quantum systems on the microwave transmitting and receiving technology.