Knowing the geographical origin of economically important plants is important for genetic improvement and conservation, but has been slowed by uneven geographical sampling where relatives occur in remote areas of difficult access. Less biased species sampling can be achieved when herbarium collections are included as DNA sources. Here, we address the history of Cucurbitaceae, one of the most economically important families of plants, using a multigene phylogeny for 114 of the 115 genera and 25 per cent of the 960 species. Worldwide sampling was achieved by using specimens from 30 herbaria. Results reveal an Asian origin of Cucurbitaceae in the Late Cretaceous, followed by the repeated spread of lineages into the African, American and Australian continents via transoceanic long-distance dispersal (LDD). North American cucurbits stem from at least seven range expansions of Central and South American lineages; Madagascar was colonized 13 times, always from Africa; Australia was reached 12 times, apparently always from Southeast Asia. Overall, Cucurbitaceae underwent at least 43 successful LDD events over the past 60 Myr, which would translate into an average of seven LDDs every 10 Myr. These and similar findings from other angiosperms stress the need for an increased tapping of museum collections to achieve extensive geographical sampling in plant phylogenetics.