Pig domestication began around 9000 YBP in the Fertile Crescent and Far East, involving marked morphological and genetic changes that occurred in a relatively short window of time. Identifying the alleles that drove the behavioural and physiological transformation of wild boars into pigs through artificial selection constitutes a formidable challenge that can only be faced from an interdisciplinary perspective. Indeed, although basic facts regarding the demography of pig domestication and dispersal have been uncovered, the biological substrate of these processes remains enigmatic. Considerable hope has been placed on new approaches, based on next-generation sequencing, which allow whole-genome variation to be analyzed at the population level. In this review, we provide an outline of the current knowledge on pig domestication by considering both archaeological and genetic data. Moreover, we discuss several potential scenarios of genome evolution under the complex mixture of demography and selection forces at play during domestication. Finally, we highlight several technical and methodological approaches that may represent significant advances in resolving the conundrum of livestock domestication.