Starting from mid-70th, a great deal of both experimental and theoretical efforts has been attracted to the unexplained puzzle of impurity states arising in the IV-VI narrow-gap cubic semiconductors doped with some of the group III elements, and to the unusual effects observed in these materials. The electrical activity of these impurities should be mentioned first. The same impurity can be either donor or acceptor depending on the specific composition of the semiconductor and on the position of the chemical potential. The variable electrical activity of the III group impurities leads to the pinning of chemical potential at any particular energy. The pinning energy can fall either in the allowed bands or in the gap depending on the type of impurity, the pressure, the magnetic field and the specific composition of semiconductor. It would appear reasonable to associate this phenomenon with the mixed-valence of the III group impurities, when the transition of electrons from the deep s-shell of an impurity atom to the Fermi level forming additional valence bonds results in the energy gain. The possibility to vary the valence of the III group impurity in the IV-VI semiconductors leads to the appearance of the metastable electron states and a number of other effects including superconductivity. Some of these effects are observed in the rather wide-bandgap III-V and IIVI semiconductors with the DX-centers in which they are usually attributed to the large lattice relaxation of the impurity crystalline environment. However a range of features, such as unusual electrical activity of impurity centers, metastability of local excited states, narrow bandgap - make the effects observed in the IV-VI semiconductors, as well as the physical picture of the processes involved, much more complicated than in the “classical” materials with the DX-centers. It is important that correlation between the characteristic time of the impurity centers recharge τ = RC and the microwave frequency corresponding to the photoconductivity quenching is established. We review the experimental results obtained in the field: the electrical activity of impurity centers, persistent photoconductivity and related effects, unusual optical, dielectric and magnetic phenomena. Some of the features of these semiconductors, such as possibility of realization of the semiinsulating state with the persistent photoresponse, possibility of fast quenching of persistent photoconductivity, microwave stimulation of the quantum efficiency up to 100, and some others, have made it possible to construct the far-infrared photodetector with extremely high characteristics. 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.