It is now 20 years since the publication of Engle's (1982) seminal paper, which introduced ARCH to the world. The ARCH paper had an enormous influence on both theoretical and applied econometrics, and was influential in the establishment of the discipline of Financial Econometrics. In this paper we provide an introduction to the special issue on modelling and forecasting financial volatility, which commemorates the Twentieth Anniversary of the publication of ARCH. Financial econometrics has become a mature discipline over the last two decades, and one of its major research objects is the modelling and forecasting of volatility. This special issue presents ten papers, all of which focus on volatility and risk. The papers examine issues such as the new frontiers of volatility, the selection of models for observed and unobserved volatility, the potential long-memory property of volatility, and the measurement of volatility. The commonality of papers is that they do not examine the extant literature, which has been reviewed elsewhere, but rather outline a number of important issues that are not only of current interest, but are likely to remain so for many years to come. Copyright © 2002 John Wiley & Sons, Ltd.