Parasitic plants in the genus Striga, commonly known as witchweeds, cause major crop losses in sub-Saharan Africa and pose a threat to agriculture worldwide. An understanding of Striga parasite biology, which could lead to agricultural solutions, has been hampered by the lack of genome information. Here we report the draft genome sequence of Striga asiatica with 34,577 predicted protein-coding genes, which reflects gene family contractions and expansions that are consistent with a three-phase model of parasitic plant genome evolution. Striga seeds germinate in response to host-derived strigolactones (SLs) and then develop a specialised penetration structure, the haustorium, to invade the host root. A family of SL receptors has undergone a striking expansion, suggesting a molecular basis for the evolution of broad host range among Striga spp. We found that genes involved in lateral root development in non-parasitic model species are coordinately induced during haustorium development in Striga, suggesting a pathway that was partly co-opted during the evolution of the haustorium. In addition, we found evidence for horizontal transfer of host genes as well as retrotransposons, indicating gene flow to S. asiatica from hosts. Our results provide valuable insights into the evolution of parasitism and a key resource for the future development of Striga control strategies.