This Book deals with implied volatility, how it is recognized, modeled, and the ways used by practitioners in order to benefit from an arbitrage opportunity when compared to the realized volatility. Prediction power of implied volatility is examined and findings of previous studies are supported, that it has the best prediction power of all existing volatility models. When regressed on implied volatility, realized volatility shows a high beta of 0.88, which contradicts previous studies that found lower betas. Moment swaps are discussed and the ways to use them in the context of volatility trading, the payoff of variance swaps shows a significant negative variance premium which supports previous findings. An algorithm to find a fair value of a structured product aiming to profit from skew arbitrage is presented and the trade is found to be profitable in some circumstances. Different suggestions to implement moment swaps in the context of portfolio optimization are also discussed.