Single-photon counting has great application prospects in weak signal detection and time ranging. Since the first photon counting system in the visible spectrum was developed in the 1970s, in order to fully amplify the photon signal and reduce the readout noise of electronic equipments, many groups in the research field are constantly developing and improving the photon counting techniques. Electron multiplying charge coupled devices (EMCCDs) can replace the traditional visible light photon counting system and have higher quantum efficiency. While due to large avalanche noise, accurate acquisition of incident photon number under multiplication is difficult. The excess noise factor of mercury cadmium telluride avalanche photodiode (HgCdTe APD) is close to 1, there is almost no excess noise. Compared with the Geiger mode avalanche photodiodes, the linear mode HgCdTe APD has no dead time and after pulse, does not need to quench the circuit, has ultra-high dynamic range and adjustable spectrum with wide response range. Its detection efficiency and false count rate can be independently optimized. It opens up a new infrared photon band counting imaging application. It is of great value in astronomical exploration, laser radar, free space communication and other applications.Raytheon and DRS Technologies in the United States, CEA/LETI Laboratory and Lynred in France, and Leonardo in the United Kingdom have successively realized single photon counting of linear HgCdTe APD detectors. This paper summarizes the technical routes and research status of linear mode photon counting HgCdTe APD detectors in Europe and America. The performance of HgCdTe APDs, photon counting ability and the advantages and disadvantages of detector preparation with three structures, namely, separation of absorption and amplification (SAM), planar PIN type and high density vertically integrated photodiode (HDVIP), are analyzed. Raytheon Company has prepared SAM short-wave HgCdTe APD detectors with hole multiplication mechanism by molecular beam epitaxy (MBE), with gain of 350, photon detection efficiency of more than 95% and operating temperature of more than 180 K. DRS Technologies has prepared an electron-multiplication HDVIP medium wave HgCdTe APD detector using liquid phase epitaxy (LPE) material. The detector can respond in the visible to mid-infrared band from 0.4 μm to 4.3 μm, with the highest gain up to 6100 and the photon detection efficiency greater than 70%. It can realize free space communication of 110 Mbps data transfer. CEA/LETI Laboratory and Lynred Company have prepared PIN-type short-wave and medium-wave HgCdTe APD detectors with electron multiplication mechanism by molecular beam epitaxy or liquid phase epitaxy. The gain of short-wave detector is up to 2 000, the maximum gain of medium-wave is up to 13000, the internal photon detection efficiency is up to 90%, the free space communication of 80 Mbps data transfer is realized, and bandwidth up to 10 GHz is achieved at 300 K and gain of 1. British Leonardo Company has prepared SAM type HgCdTe APD detector with electron multiplication mechanism by metal organic vapor deposition (MOVPE). The detectors were named Selex Avalanche Photodiode HgCdTe Infrared Array (SAPHIRA), the device gain can reach 66@14.5 V, single photon detection efficiency is more than 90%. A 24 μm pitch 320×256 array SAPHIRA detectors were supplied to First Light Imaging Company in France to develop a C-RED ONE camera. The C-RED ONE camera was successfully applied to the Michigan Infrared Combiner (MIRC) for astronomical exploration in the United States, which reduced the system noise of MIRC by 10 to 30 times and greatly improved the signal-to-noise ratio of fringe detection. The research on HgCdTe APD detectors started relatively late in China. The main research institutions include Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Kunming Institute of Physics and North China Research Institute of Electro-Optics. Limited by chip preparation technology and circuit technology of HgCdTe APDs, the ability of photon counting has not been realized at present, but some progress has been made in the development of focal plane at home. The single element, 128×128 array and 320×256 array medium wave HgCdTe APD detectors with PIN structure are developed by Shanghai Institute of Technical Physics, Chinsese Academy of Sciences. The gain of the detectors can reach more than 1000, the gain normalized dark current density is less than 1×10^-7 A/cm² within the gain of 100, and the excess noise factor is less than 1.5 within the gain of 400. At the gain of 133, the noise equivalent photon number is 12, and the short integration time fast imaging is demonstrated. Bandwidth of single element detector is up to 300-600 MHz. The single element and 256×256 array medium wave HgCdTe APD device with PIN structure are developed in Kunming Institute of Physics. The gain of the single element detector can reach more than 1 000. When the bias voltage is less than 8.5 V, the average gain normalized dark current of focal plane is 9.0×10^-14-1.6×10^-13 A, and the excess noise factor F is between 1.0 and 1.5. In China, HgCdTe APD devices with planar PIN structure are mainly developed, and the technical path is basically the same as that of France. Therefore, our country can learn from the successful experience of CEA/LETI Laboratory and the business model of Lynred Company, and continue to promote research on HgCdTe APD detectors in order to reach the international advanced level as soon as possible, and realize single-photon detection and photon counting application.