The popularity of volatility derivatives has increased through these years of financial turmoil. In particular, variance and volatility swap seem interesting to analyse due to its growing trading volume. Hence, the aim of this work is to present a full revision of these two volatility derivatives, comparing pricing methodologies, like Taylor expansion and Heston (1993) volatility process. In addition, there will be a complete section dedicated to the study of the volatility skew and the wings or “smile”. The results showed that the Taylor expansion has a reasonable level of convergence at some values of the parameters of the volatility dynamics, though the findings concluded that higher order of this expansion yielded poor results than the lower order. In the other hand, the smile and the volatility skew showed that the former may change the final value of the fair volatility strike, whereas the latter has almost null impact on this one.