In recent years, the field of financial econometrics has seen tremendous gains in the amount of data available for use in modeling and prediction. Much of this data is very high frequency, and even “tick-based,” and hence falls into the category of what might be termed “big data.” The availability of such data, particularly that available at high frequency on an intra-day basis, has spurred numerous theoretical advances in the areas of volatility/risk estimation and modeling. In this chapter, we discuss key such advances, beginning with a survey of numerous nonparametric estimators of integrated volatility. Thereafter, we discuss testing for jumps using said estimators. Finally, we discuss recent advances in testing for co-jumps. Such co-jumps are important for a number of reasons. For example, the presence of co-jumps, in contexts where data has been partitioned into continuous and discontinuous (jump) components, is indicative of (near) instantaneous transmission of financial shocks across different sectors and companies in the markets; and hence represents a type of systemic risk. Additionally, the presence of co-jumps across sectors, say, suggests that if jumps can be predicted in one sector, then such predictions may have useful information for modeling variables such as returns and volatility in another sector. As an illustration of the methods discussed in this chapter, we carry out an empirical analysis of DOW and NASDAQ stock price returns.