When considering the dynamics of regional growth rates, one usually observes growth convergence on spatial aggregates but non-convergence or even divergence within smaller regions of different type. This book suggests various approaches to investigate this puzzle. A formal model, merging approaches from growth theory and new economic geography, shows that spatial knowledge spillovers might be the driving force behind this behavior. To analyze an arbitrary number of regions, the model is implemented on a locally recursive simulation tool - cellular automata. Convergence regressions from different runs of the automaton confirm previous findings. Finally, the existence of spatial knowledge spillovers is tested. Regressions give strong evidence for spatial knowledge spillovers. All the relevant literature and spatial econometric methods are surveyed. Data is reproduced in the appendix.