The paper presents a review of dynamic stabilization mechanisms for plasma instabilities. One of the dynamic stabilization mechanisms for plasma instability was proposed in the paper [Kawata, Phys. Plasmas 19, 024503 (2012)], based on a perturbation phase control. In general, instabilities emerge from the perturbations. Normally the perturbation phase is unknown, and so the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superimposition of perturbations imposed actively. Based on this mechanism we present the application results of the dynamic stabilization mechanism to the Rayleigh–Taylor instability (RTI) and to the filamentation instability as typical examples in this paper. On the other hand, in the paper [Boris, Comments Plasma Phys. Control. Fusion 3, 1 (1977)] another mechanism was proposed to stabilize RTI, and was realized by the pulse train or the laser intensity modulation in laser inertial fusion [Betti et al., Phys. Rev. Lett. 71, 3131 (1993)]. In this latter mechanism, an oscillating strong force is applied to modify the basic equation, and consequently the new stabilization window is created. Originally the latter was proposed by Kapitza. We review the two stabilization mechanisms, and present the application results of the former dynamic stabilization mechanism.