The limited grid resolution used for dynamic reservoir simulations has contributed to convey the perception that fluid flood fronts have fairly smooth shapes. However it has been known for a long time that reservoir permeability heterogeneities create fractal-like fluid front surfaces. Many sandstone reservoirs and most carbonate reservoirs are known to be highly heterogeneous. Fractures, texture, depositional facies, diagenesis are well known causes of heterogeneity in carbonates. In this paper we present new results of computer simulations at high grid resolution of water flood fronts in reservoirs with heterogeneous wettability distributions. Wettability is an important factor in carbonate reservoirs and these simulations clearly show the critical impact of heterogeneous wettability distributions on sweep efficiency and recovery factors. Also discussed are results for reservoirs combining heterogeneities of various origins such as matrix permeability, wettability and large scale heterogeneities such as fracture corridors. The geometry of fluid fronts predicted by these simulations is compared with actual fluid fronts monitored using advanced processing technology of high resolution 4D seismic. We also review how saturation profiles in swept zones can be estimated using well-to-well electro-magnetic image cross-sections. Finally, the impact of complex front shapes on sweep efficiencies, recovery factors, water breakthrough predictions and water cut curves versus time is discussed. Examples of possible production scenarios using intelligent completions and fluid front monitoring techniques to maximize recovery in spite of reservoir heterogeneities are presented.