Single-photon detectors based on superconducting nanowires (SSPDs or SNSPDs) have rapidly emerged as a highly promising photon-counting technology for infrared wavelengths. These devices offer high efficiency, low dark counts and excellent timing resolution. In this review, we consider
the basic SNSPD operating principle and models of device behaviour. We give an overview of the evolution of SNSPD device design and the improvements in performance which have been achieved. We also evaluate device limitations and noise mechanisms. We survey practical refrigeration technologies
and optical coupling schemes for SNSPDs. Finally we summarize promising application areas, ranging from quantum cryptography to remote sensing. Our goal is to capture a detailed snapshot of an emerging superconducting detector technology on the threshold of maturity.