Unstructured/semi-structured spatially adaptive grids are still lacking application to full-field hydrocarbon reservoir simulation, in spite of the fact that these discretisation techniques are perhaps the most important technological advancement not yet introduced into reservoir engineering during the last two decades. Only with unstructured spatially adaptive grids, complex fault arrays, facies architecture, folds or well completions can be resolved accurately. This thesis compares different gridding technologies, highlighting the advantages and challenges associated with the use of adaptive grids, and illustrating them with two-dimensional reservoir geometry examples. Using structured grids, extreme simplifications have to be made of the reservoir geometry and its stratigraphy. Ensuing differences in the flow behavior are demonstrated in a field study of the Trattnach reservoir.