Experimental and theoretical work on the ionization of deep impurity centres in the alternating terahertz field of high-intensity far-infrared laser radiation, with photon energies tens of times lower than the impurity ionization energy, is reviewed. It is shown that impurity ionization is due to phonon-assisted tunnelling which proceeds at high electric field strengths into direct tunnelling without involving phonons. In the quasi-static regime of low frequencies the tunnelling probability is independent of frequency. Carrier emission is accomplished by defect tunnelling in configuration space and electron tunnelling through the potential well formed by the attractive force of the impurity and the externally applied electric field. The dependence of the ionization probability on the electric field strength permits one to determine defect tunnelling times, the structure of the adiabatic potentials of the defect, and the Huang-Rhys parameters of electron-phonon interaction. Raising the frequency leads to an enhancement of the tunnelling ionization and the tunnelling probability becomes frequency dependent. The transition from the frequency-independent quasi-static limit to frequency-dependent tunnelling is determined by the tunnelling time which is, in the case of phonon-assisted tunnelling, controlled by the temperature. This transition to the high-frequency limit represents the boundary between semiclassical physics, where the radiation field has a classical amplitude, and full quantum mechanics where the radiation field is quantized and impurity ionization is caused by multiphoton processes. In both the quasi-static and the high-frequency limits, the application of an external magnetic field perpendicular to the electric field reduces the ionization probability when the cyclotron frequency becomes larger than the reciprocal tunnelling time and also shifts the boundary between the quasi-static and the frequency-dependent limits to higher frequencies. At low intensities, ionization of charged impurities may also occur through the Poole-Frenkel effect by thermal excitation over the potential well formed by the Coulomb potential and the applied electric field. Poole-Frenkel ionization precedes the range of phonon-assisted tunnelling on the electric field scale and enhances the ionization probability at low electric field strengths. Applying far-infrared lasers as sources of a terahertz electric field, the Poole-Frenkel effect can clearly be observed, allowing one to reach a conclusion regarding the charge of deep impurities.