The paper reviews a novel class of phenomena observed recently in the two-dimensional (2D) electron system formed on the free surface of liquid helium in the presence of a magnetic field directed normally and exposed to microwave radiation. The distinctive feature of these nonequilibrium phenomena is magnetoconductivity oscillations induced by inter-subband (out-of-plane) and intra-subband (in-plane) microwave excitations. The conductivity magneto-oscillations induced by intra-subband excitation are similar to remarkable microwave-induced resistance oscillations (MIRO) reported for semiconductor heterostructures. Investigations of microwave-induced conductivity oscillations (MICO) on liquid helium helped with understanding of the origin of MIRO. Much stronger microwaveinduced conductivity oscillations were observed and well described theoretically for resonant inter-subband microwave excitation. At strong powers, such excitation leads to zero-resistance states (ZRS), the in-plane redistribution of electrons, self-generated audio-frequency oscillations, and incompressible states. These phenomena are caused by unusual current states of the 2D electron system formed under resonant microwave excitation.Keywords Magneto-oscillations · 2D electron gas · Liquid helium 1 Introduction A two-dimensional (2D) electron gas on the free surface of liquid helium is formed by a one-dimensional (1D) potential well V (z) created by a weak polarization attraction of an electron to the liquid medium and by a strong repulsion barrier