Volatility ranks among the most active and successful areas of research in econometrics and empirical asset pricing finance over the past three decades. This research review studies and analyses some of the most influential published works from this burgeoning literature, both classic and contemporary. Topics covered include GARCH, stochastic and multivariate volatility models as well as forecasting, evaluation and high-frequency data. This insightful review presents and discusses the most important milestones and contributions that helped pave the way to today's understanding of volatility.