The plant family Orobanchaceae includes many parasitic weeds that are also impressive invaders and aggressive crop pests with several specialized features (e.g. microscopic seeds, parasitic habits). Although they have provoked several large-scale eradication and control efforts, no global evaluation of their invasive potential is as yet available. We use tools from ecological niche modeling in combination with occurrence records from herbarium specimens to evaluate the global invasive potential of each of 10 species in this assemblage, representing several of the worst global invaders. The invasive potential of these species is considerable, with all tropical and subtropical countries, and most temperate countries, vulnerable to invasions by one or more of them.