Light detection is the underlying principle of many optoelectronic systems. For decades, semiconductors including silicon carbide, silicon, indium gallium arsenide and germanium have dominated the photodetector industry. They can show excellent photosensitivity but are limited by one or more aspects, such as high production cost, high-temperature processing, flexible substrate incompatibility, limited spectral range or a requirement for cryogenic cooling for efficient operation. Recently lead sulphide (PbS) nanocrystals have emerged as one of the most promising new materials for photodetector fabrication. They offer several advantages including low-cost manufacturing, solution processability, size-tunable spectral sensitivity and flexible substrate compatibility, and they have achieved figures of merit outperforming conventional photodetectors. We review the underlying concepts, breakthroughs and remaining challenges in photodetector technologies based on PbS nanocrystals.