With the development of the financial industry and the improvement of financial markets, the security market becomes more and more important in people's life. As the basis for existence and development of the stock market, volatility has increasingly become the focus of financial economics. However, the perspective, methods and conclusions are quite different in these studies. This paper summarizes the literatures about the volatility of stock market in the recent twenty years both home and abroad, and furthermore brings up the underlying problems in the past studies.