The objective of this thesis is to give a description of the rough stochastic volatility modelling based on fractional Brownian motion with Hurst exponent H less than 1/2, as well as the corresponding pricing model. Specifically we considered the Rough Fractional Stochastic Volatility (RFSV) model that is proposed in Gatheral et al. (2014), we presented and verified its findings. The thesis starts with a review of some significant volatility and pricing models, for some of them we covered the details of the mathematical derivations. The stochastic calculus with respect to fractional Brownian motion is also provided.