The article reviews the theory of a number of phenomena occurring in a plasma situated in a strong high-frequency field. The analysis is based on a relatively simply hydrodynamic collisionless plasma model. Principal attention is paid to the stability of the plasma in the strong high-frequency field. A single dispersion equation is used to consider different modifications of parametric instabilities (decay instabilities, parametric resonance, transparent-plasma instability of the stimulated scattering type). Also discussed are a number of problems in the equilibrium and dynamics of a plasma in a strong high-frequency field, particularly nonlinear penetration and reflection of electromagnetic waves from a plasma, stationary nonlinear waves, and spreading and contraction of a plasma layer under the influence of the pressure of a high-frequency field.