With the rapid development of single-photon detectors and technologies, single-photon LiDAR with photon-level sensitivity has become a popular research topic. It plays an increasingly important role in fields such as remote sensing and mapping, intelligent driving, and consumer electronics. This paper focuses on LiDAR technologies and systems employing single-photon avalanche diode detectors, introducing three single-photon LiDAR detection principles: pulse accumulation, coding modulation and chirp modulation. Considering the importance of detectors and algorithms, it outlines the current development status of single-photon detectors and typical processing algorithms. It also reviews the applications and typical systems of single-photon LiDAR in long-distance detection, complex scene sensing, satellite/airborne remote sensing and mapping, intelligent driving navigation and obstacle avoidance, and 3D sensing in consumer electronics. Lastly, the paper analyzes the future development trends and forecasts the potential challenges of single-photon LiDAR technology in detectors, algorithms, systems, and application domains.