This thesis mainly concerns some novel developments in volatility modelling. We first derive the diffusion limits of two recently proposed (discrete time) volatility models. Subsequently, we propose a new model that allows for conditional heteroskedasticity in the volatility of asset returns and incorporates current return information into the volatility nowcast and forecast. Our model can capture most stylised facts of asset returns even with Gaussian innovations and is simple to implement. Moreover, we show that our model converges weakly to the GARCH-type diffusion as the length of the discrete time intervals between observations goes to zero. Finally, we generalise our model and propose a new class of volatility models in which we can directly model the time-varying volatility of volatility. We also derive some statistical properties regarding this class of models. Empirical evidence shows that this class of models has better fits as well as more accurate volatility and VaR forecasts than other common GARCH-type models.