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Cross-coupling is one of the most successful strategies for the efficient generation of new carbon-carbon bonds. It involves the reaction between molecules containing C-X and C-Y bonds, where X is more electronegative and Y more electropositive than carbon. The scope of cross-coupling is limited by the relative scarceness of C-Y bonds in most chemical reagents, which have thus to be modified before cross -coupling. This can be overcome by oxidative coupling, where no electropositive Y group is necessary. Oxidative coupling needs however an external oxidant. We have made in the past a number of computational contributions to the mechanistic understanding of cross-coupling which will be briefly reviewed. The focus of the talk will be on the recent extension of these mechanistic studies to the case of oxidative coupling.