This paper, prepared for the Handbook of Statistics, vol.14, Statistical Methods in Finance, surveys the subject of Stochastic Volatility. The following subjects are covered : volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and finally statistical inference ( methods of moments, Quasi-Maximum-Likelihood, Likelihood based and Bayesian Methods and Indirect Inference).