Doping of the lead telluride and related alloys with the group III impurities results in appearance of the unique physical features of a material, such as persistent photoresponse, enhanced responsive quantum efficiency (up to 100 photoelectrons/incident photon), radiation hardness and many others. We present the physical principles of operation of the photodetecting devices based on the group III-doped IV-VI including the possibilities of a fast quenching of the persistent photoresponse, construction of the focal-plane array, new readout technique, and others. The advantages of infrared photodetecting systems based on the group III-doped IV-VI in comparison with the modern photodetectors are summarized. The theoretical models proposed so far to account for the physical picture of the processes involved are discussed in view of the recent advances in the field. We present results on direct comparison of performance for a Pb1-xSnxTe(In) photodetector, and state-of the art Si(Sb) and Ge(Ga) photodetectors. The same cryogenic environment and measuring electronics was used for testing of all photodetectors mentioned above. The Pb1-xSnxTe(In) photodetector shows several orders of magnitude higher responsivity SI then the Si(Sb) detector at the wavelength ~ 14 microns. Persistent photoresponse at the wavelengths of up to 240 microns has been observed for the Pb1-xSnxTe(In) photodetector, which is higher than the highest cutoff wavelength observed so far for the photon detectors of TeraHertz radiation. The presented new type of detectors of TeraHertz radiation represents a challenging alternative to the existing analogs, especially for spectroscopic and space-borne applications.