Volatilities of asset returns are central to the theory and practice of asset pricing, portfolio allocation, and risk management. In financialeconomics, there is extensive research on modeling and forecastingvolatility based on Black-Scholes, diffusion, GARCH, stochastic volatilitymodels and option pricing formulas. Nowadays, thanks to technologicalinnovations, high-frequency financial data are available for a host ofdifferent financial instruments on markets of all locations and at scaleslike individual bids to buy and sell, and the full distribution of suchbids. The availability of high-frequency data stimulates an upsurgeinterest in statistical research on better estimation of volatility. This talk will start with a review on low-frequency financial time series andhigh-frequency financial data. Then I will introduce popular realizedvolatility computed from high-frequency financial data and present my workon wavelet methods for analyzing jump and volatility variations and thematrix factor model for handling large size volatility matrices. Theproposed wavelet based methodology can cope with both jumps in the priceand market microstructure noise in the data, and estimate both volatilityand jump variations from the noisy data. The matrix factor model isproposed to produce good estimators of large size volatility matrices byattacking non-synchronized problem in high-frequency price data and reducing the huge dimension (or size) of volatility matrices. Parts of mytalk are based on joint work with Jianqing Fan, Qiwei Yao, and Pengfei Li.