Pandanaceae (screwpines) is a monocot family composed of c. 750 species widely distributed in the Paleotropics. It has been proposed that the family may have a Gondwanan origin with an extant Paleotropical distribution resulting from the breakup of that supercontinent. However, fossils supporting that hypothesis have been recently reassigned to other families while new fossil discoveries suggest an alternate hypothesis. In the present study, nuclear and chloroplast sequences were used to resolve relationships among Pandanaceae genera. Two well-supported fossils were used to produce a chronogram to infer whether the age of major intra-familial lineages corresponds with the breakup of Gondwana. The Pandanaceae has a Late Cretaceous origin, and genera on former Gondwanan landmasses began to diverge in the Late Eocene, well after many of the southern hemisphere continents became isolated. The results suggest an extant distribution influenced by long-distance-dispersal. The most widespread group within the family, the Pandanus tectorius species complex, originated in Eastern Queensland within the past six million years and has spread to encompass nearly the entire geographic extent of the family from Africa through Polynesia. The spread of that group is likely due to dispersal via hydrochory as well as a combination of traits such as agamospermy, anemophily, and multi-seeded propagules which can facilitate the establishment of new populations in remote locations.