Geological modelling and flow simulation in the subsurface in heterogeneous and anisotropic media is increasingly common. Unfortunately, conventional modelling using statistical techniques, up-scaling and interpolation to populate the inter-well volume of sparse datasets have a low resolution (> 50 m). Consequently they have difficulty modelling heterogeneous and anisotropic reservoirs. This paper focusses on modelling and simulation of heterogeneous and anisotropic reservoirs using a fractal approach (Advanced Fractal Reservoir Models; AFRMs), which includes variability at all scales such that it can represent the heterogeneity correctly at each scale. These three-dimensional AFRMs can be used to model any fractally complex volume with applications well outside geosciences. In our application AFRMs can be used in generic modelling to understand the effects of heterogeneity and anisotropy, but can also be conditioned to represent real reservoirs. This paper will show how 3D AFRMs can be constructed to represent reservoir parameters (e.g., porosity, permeability, water saturation, relative permeabilities). Results of generic modelling and simulation with AFRMs will be given for a 2 phase system, which show how total and incremental fluid flow and breakthrough all depend strongly on heterogeneity as represented by the fractal dimension the reservoir, and also depends upon anisotropy. The real test of AFRMs is their capacity to be conditioned to real scenarios. Results for moderate to high heterogeneity reservoirs comparing the flow characteristics of such an approach to a conventional kriging/upscaling show that AFRMs was always within 5% of ideal, compared with underestimations by over 70% for the conventional approach.