Abstract: We present an overview of the state-of-the-art of NbN superconducting single-photon detectors (SSPDs). Our devices exhibit quantum efficiency (QE) of up to 30% in near-infrared wavelength and 0.4% at 5 mum, with a dark-count rate that can be as low as 10 -4 s -1 . The SSPD structures integrated with lambda/4 microcavities achieve a QE of 60% at telecommunication, 1550-nm wavelength. We have also developed a new generation of SSPDs that possess the QE of large-active-area devices, but, simultaneously, are characterized by low kinetic inductance that allows achieving short response times and the GHz-counting rate with picosecond timing jitter. The improvements presented in the SSPD development, such as fiber-coupled SSPDs, make our detectors most attractive for high-speed quantum communications and quantum computing.