Traditionally, the process of domestication is assumed to be initiated by humans, involve few individuals and rely on reproductive isolation between wild and domestic forms. We analyzed pig domestication using over 100 genome sequences and tested whether pig domestication followed a traditional linear model or a more complex, reticulate model. We found that the assumptions of traditional models, such as reproductive isolation and strong domestication bottlenecks, are incompatible with the genetic data. In addition, our results show that, despite gene flow, the genomes of domestic pigs have strong signatures of selection at loci that affect behavior and morphology. We argue that recurrent selection for domestic traits likely counteracted the homogenizing effect of gene flow from wild boars and created 'islands of domestication' in the genome. Our results have major ramifications for the understanding of animal domestication and suggest that future studies should employ models that do not assume reproductive isolation.