Electron cyclotron resonance heating (ECRH) is a technique being widely utilized nowadays in magnetic fusion experiments. It is also considered for application in ITER, for plasma heating and neoclassical tearing mode control. The analysis [1][2][3] of different parametric decay instabilities (PDIs) potentially dangerous for mm-waves at the ECR frequencies in the presence of the monotonous plasma profiles revealed the typical microwave power threshold in the range much higher than 1 MW. This is due to huge energy loss of the interacting waves from the decay region. The typical heating system output power range available up to now, even if the gyrotrons are joined into a group, is substantially lower than the predicted PDI power threshold value. Thus, it has been taken as known until very recently that the ordinary or extraordinary electromagnetic wave propagation and absorption in the absence of the UHR being well described by linear theory is predictable in detail.However, during the last decade many observations have demonstrated the anomalous phenomena during ECRH. Firstly, the fast ion generation and ion heating were observed at the TJ-II stellarator [4] and the TCV tokamak [5] during the 2 nd harmonic Xmode ECRH pulse under conditions when energy exchange between electrons and ions should be very low. Secondly, the observations of the backscattering signal down -shifted from the pump frequency by approximately 1 GHz and correlated to the MHD mode rotation were reported [6,7] in the 200 -600 kW level 2 nd harmonic X-mode ECRH experiment in the TEXTOR tokamak and interpreted in terms of anomalous backscattering of the pump EC wave. The anomalous scattering of the X-mode in the ASDEXUpgrade tokamak 2 nd harmonic ECRH experiment has been recently reported as well [8,9].The attempts of theoretical explanation of these anomalous phenomena have been undertaken during recent years [10][11][12][13]. Several theoretical models demonstrating the possibility of excitation of the lowthreshold PDIs which lead to generation of the electron and ion Bernstein waves had been proposed. The cornerstone of them is taking full account of a nonmonotonous plasma density profile often observed in the ECRH experiments and originated due to different physical mechanisms, among which are features of plasma confinement in the magnetic island [14] or the electron pump-out effect manifesting itself as a consequence of the anomalous convective particle flux from the ECR layer at the intensive ECRH. The poloidal magnetic field inhomogeneity is a key element of the theory as well. Based on these two elements it was shown that two-or even three-dimensional (2D or 3D) trapping of either a daughter ion Bernstein wave (IBW) or a daughter electron Bernstein wave (EBW) due to a specific multidimensional plasma inhomogeneity can be responsible for excitation of several convective and absolute PDIs possessing thresholds drastically less than those predicted by the standard model.These theoretical results expanded significantly the standard theory w...