In the last decade the hedge fund industry has been the fastest growing asset class in the financial sector. Low volatility and low correlation, together with historically good performance may explain the increasing attractiveness of hedge funds among insitutional and retail investors in recent years. However, hedge funds pose a challenge to standard risk measures based on normally distributed returns. Indeed, the returns of hedge fund indices are not normally distributed and have exhibited unusuall levels of skewness and kurtosis. Clearly, volatility and correlation do not provide sufficient information about risk and dependence when the normality assumption is violated. As a consequence, applying symmetric measures on hedge funds may lead to erroneous conclusions. In this thesis, the use of Extreme Value Theory is advocated. This area of statistics enables the estimation of tail probabilities regardless of the underlying distribution of hedge fund returns. This thesis contributes to the growing literature onn risk associated with hedge funds in two main directions. Firstly, it carefully examines the tail risk of individual hedge fund strategies and of portfolios built with stocks, bonds and hedge funds using Extreme Value Theory. Secondly, it furhter measures the dependence between hedge funds and traditional investments in period of crises. For this purpose it tests explicitly the existence of asymptotic dependence between hedge funds and traditional investments.