Abstract. Alien grass species have been intentionally introduced into Australia since European settlement over 200 years ago, with many subsequently becoming weeds of natural environments. We have identified the subset of these weeds that have invaded and become dominant in environmentally important areas in the absence of modern anthropogenic disturbance, calling them 'high-impact species'. We also examined why these high-impact species were successful, and what that might mean for management. Seventeen high-impact species were identified through literature review and expert advice; all had arrived by 1945, and all except one were imported intentionally, 16 of the 17 were perennial and four of the 17 were aquatic. They had become dominant in diverse habitats and climates, although some environments still remain largely uninvaded despite apparently ample opportunities. Why these species succeeded remains largely untested, but evidence suggests a combination of ecological novelty (both intended at time of introduction and unanticipated), propagule pressure (through high reproductive rate and dominance in nearby anthropogenically-disturbed habitats) and an ability to respond to, and even alter, natural disturbance regimes (especially fire and inundation). Serious knowledge gaps remain for these species, but indications are that resources could be better focused on understanding and managing this limited group of high-impact species. They require new management approaches, especially to counteract the advantages of ecological novelty, reduce propagule pressure and better direct the large-scale disturbance regimes that continue to shape plant communities across Australia.