Abstract: The superconducting nanowire single-photon detector (SNSPD) represents a novel class of single-photon detection devices. Compared with traditional single-photon detectors, it has advantages such as high detection efficiency, low dark count rate, high count rate and low timing jitter. In recent years, it has made remarkable achievements in fields like quantum information and laser radar. With the advancement of technology, applications such as quantum communication and deep-space laser communication have imposed higher requirements on the response speed (i.e. count rate) of SNSPDs. This paper first provides a brief introduction to the basic principles of SNSPDs, and then focuses on the research progress of high-speed SNSPDs. It mainly includes the factors restricting the count rate of SNSPDs and several methods to increase the count rate. Finally, the future development trends of high-speed SNSPDs are prospected.