A survey of stochastic averaging methods in random vibration is given. After a brief introduction to the basic ideas, the advantages and the history of the methods, three kinds of stochastic averaging methods are formulated, and their applicability and recent developments are stated. In the second part, the applications of the methods in response prediction, stability decision, and reliability estimation of randomly excited nonlinear and parametric systems are reviewed. The possibility of further developments and applications of the methods is also pointed out.