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 spectra of the persistent photoresponse have not been measured so far because of the difficulties with screening the background radiation. We report on the observation of strong persistent photoconductivity in Pb_0.75Sn_0.25Te(In) under the action of monochromatic submillimeter radiation at wavelengths of 176 and 241 microns. The sample temperature was 4.2 K, the background radiation was completely screened out. The sample was initially in the semiinsulating state providing dark resistance of more than 100 GOhm. The responsivity of the photodetector is by several orders of magnitude higher than in the state of the art Ge(Ga). The red cut-off wavelength exceeds the upper limit of 220 microns observed so far for the quantum photodetectors in the uniaxially stressed Ge(Ga). It is possible that the photoconductivity spectrum of Pb_1-xSn_xTe(In)covers all the submillimeter wavelength range.