We in this thesis study the dynamics of volatility skew in the foreign exchange market. Real market data from the foreign exchange market is used to isolate and describe the dynamic patterns of the volatility surface. We also present a class of models that reproduces the same type of dynamics that we observe in the market. The class is based on the concept of stochastic volatility where skew dynamics is introduced by making the correlation between the spot price and the volatility stochastic. This way the market is described by three stochastic diffusion processes. A specific model choice is considered and a numerical scheme to price options under this model is presented. Further the impact if making correlation between the spot level and the volatility stochastic is investigated for vanilla options, American barrier options (also known as one-touch options), forward starting options and partial time knock-out options. We find that the new model reproduces phenomena observed in the real market not explained by previously published models.