Approximately 200 weed species are responsible for more than 90% of crop losses and these comprise less than one percent of all named plant species, suggesting that there are only a few evolutionary routes that lead to weediness. Agricultural weeds can evolve along three main paths: they can be escaped crops, wild species, or crop-wild hybrids. We tested these three hypotheses in weedy radish, a weed of small grains and an emerging model for investigating the evolution of agricultural weeds, using 21 CAPS and SSR markers scored on 338 individuals from 34 populations representing all major species and sub-species in the radish genus Raphanus. To test for adaptation of the weeds to the agricultural environment, we estimated genetic differentiation in flowering time in a series of common garden experiments with over 2400 individuals from 43 populations (all but one of the genotyped populations plus 10 additional populations). Our findings suggest that the agricultural weed radish R.r. raphanistrum is most genetically similar to native populations of R.r. raphanistrum, and is likely not a feral crop or crop hybrid. We also show that weedy radish flowers more rapidly than any other Raphanus population or cultivar, which is consistent with rapid adaptation to the frequent and severe disturbance that characterizes agricultural fields.