The review aims to present the current state of research on the resonance plasma heating by high-power laser radiation in the presence of a strong magnetic field. It is demonstrated that modulation instability with a modulation period equal to the wavelength of the driven plasma wave occurs upon propagation of a low-amplitude pulse parallel to the magnetic field in a subcritical-density plasma in the ECR region. The magnitude of the driven longitudinal electric field grows substantially with increase in the pulse amplitude. In the process, the energy imparted to plasma electrons by the laser radiation increases severalfold relative to the case of an isotropic plasma. The physical mechanism of strong heating of electrons consists in transformation of the modulation instability into stochastic regime at high amplitudes. Propagation of an extraordinary laser wave in plasma in the region of parametric resonance at twice the upper hybrid frequency is analyzed in the case of wave propagation perpendicular to the magnetic field. Considerable auxiliary heating of electrons due to laser-wave decay into upper hybrid plasmons and excitation of the Bernstein waves takes place under such interaction as well. It follows from the electric-field distribution at the time of laser pulse arriving to the right boundary of the plasma layer that strong absorption of the transverse electric field of the laser pulse and enhancement of the longitudinal field occur in the region of parametric upper-hybrid resonance, which is accompanied by the appearance of the reflected electromagnetic wave at the upper hybrid frequency.