We present a brief review of activity towards the resonant state THz laser on strained p-Ge and boron doped strained Si1-xGex quantum well structure. The mechanism of THz lasing is the formation of population inversion of the resonant state with respect to the localized state of the same impurity. The new method for calculating the parameters of resonant state as well as the probability of resonant scattering, capture and emission is developed. It is based on configuration interaction method, which was first introduced by Fano in the problem of autoionization of He. The method has been applied to resonant states induced by shallow acceptors in Ge under stress, where CW and pulse THz lasing has been observed. Intense stimulated emission in the frequency range between 3 and 6 THz has been recently observed in Si1-xGex QW structure.