Ultra-sensitive single-photon detection is a key technology for the development of optical quantum information and quantum manipulation. It is of important scientific significance and application value to realize high-efficiency, high-sensitivity, low-power and low-cost single-photon photodetectors. There is still a large gap between visible single-photon detector based on silicon and infrared ones in terms of the cost and performance. Exploring the technology of infrared single-photon detection with novel materials and mechanism has become the urgent needs in the field of photodetection. In recent years, low-dimensional materials have offered a new possibility for realizing high-gain, room-temperature and broad-band photodetectors due to their unique physical and chemical properties. The research on the low-dimensional materials based photodetectors with good performance has also become a hot topic in the field of infrared photodetection. In this review, the basic principles of traditional avalanche infrared photodetectors were introduced firstly. On this basis, the latest development of avalanche devices based on novel low-dimensional materials was summarized. Then the new gain amplification mechanism of the photodetector based on photogating effect was discussed and the structure as well as the performance of the devices were reviewed. Finally, the future developing directions and challenges of the infrared single-photon detection technology were prospected.