Crude oil markets are highly volatile and risky. Extreme Value Theory (EVT), an approach to modelling and estimating risks under rare events, has seen a more prominent role in risk management in recent years. This Book presents an application of EVT to the daily returns of Brent crude oil prices in the spot market between 1987 and 2009. We focus on the peak over threshold method by analysing the generalized Pareto distributed exceedances over some high threshold. This method provides an effective means for estimating tail risk measures specifically, Value-at-Risk (VaR) and Expected Shortfall (ES). The estimates of these risk measures computed under high quantile ie, at the 99th quantile provides the estimates of VaR approximately as 8.1% and 8.0% for daily positive and negative returns, respectively. The estimates for expected shortfall are 12.3% and 10.7% for daily positive and negative returns, respectively.