The authors survey the theory of parametric instabilities of a plasma in a high-frequency electric field. The general features of the decay instability of low-amplitude pump waves are illustrated on the basis of a simple model of a wave medium with wave phase velocity periodic in time. The changes in the nature of the instability with increasing pump wave amplitude are discussed. Instability thresholds have been found with allowance for the dissipation and convection of perturbations in an inhomogeneous plasma. The authors have taken into consideration the latest advances in the formulation of a nonlinear theory of parametric instabilities based on the theory of weakly turbulent plasma. In particular, the effective frequencies of collisions characterizing the absorption of high-frequency field energy by a plasma have been found. The paper also discusses the problems of the existing theory, viz. the appearance of non-Maxwellian tails in the electron distribution, the formation of plasmon condensates in a plasma with rare collisions, and so on.The authors illustrate the application of the methods that have been developed to other aspects of the mechanics of continuous media, using as an example the dynamics of waves on the surface of a liquid. The interrelationship between the theories of wave stability developed by specialists in mechanics and plasma physicists is discussed.