Traditionally, the process of domestication is assumed to be initiated by people, involve few individuals and rely on reproductive isolation between wild and domestic forms. However, an emerging zooarcheological consensus depicts animal domestication as a long-term process without reproductive isolation or strong intentional selection. Here, we ask whether pig domestication followed a traditional linear model, or a complex, reticulate model as predicted by zooarcheologists. To do so, we fit models of domestication to whole genome data from over 100 wild and domestic pigs. We found that the assumptions of traditional models, such as reproductive isolation and strong domestication bottlenecks, are incompatible with the genetic data and provide support for the zooarcheological theory of a complex domestication process. In particular, gene-flow from wild to domestic pigs was a ubiquitous feature of the domestication of pigs. In addition, we show that despite gene-flow, the genomes of domestic pigs show strong signatures of selection at loci that affect behaviour and morphology. Specifically, our results are consistent with independent parallel sweeps in two independent domestication areas (China and Anatolia) at loci linked to morphological traits. We argue that recurrent selection for domestic traits likely counteracted the homogenising effect of gene-flow from wild boars and created "islands of domestication" in the genome. Overall, our results suggest that genomic approaches that allow for more complex models of domestication to be embraced should be employed. The results from these studies will have significant ramifications for studies that attempt to infer the origin of domesticated animals.