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Abstract Aim To determine the evolutionary history of the widely studied, cosmopolitan polymorphic species Dodonaea viscosa (hop bush, varnish tree). Location All continents except Antarctica, extending from 44° S (in the South Island of New Zealand) to 33° N (in California and Arizona). Methods For 50 samples across the worldwide distribution, Bayesian analyses of nuclear ribosomal transcribed spacers (ITS 1, ITS 2 and partial ETS) were performed. The alignment was partitioned by secondary structure and analysed using separate models of sequence evolution for each spacer’s stem and loop partition. Bayesian relaxed-clock estimations of divergence times were used to investigate the tempo of the transoceanic dispersal history of Dodonaea viscosa. Results The widely distributed Dodonaea viscosa evolved in Australia from its most recent common ancestor in the Late Pliocene to Early Pleistocene and subsequently split into two distinct, geographically based, intraspecific lineages. There are a number of regional subclades that are also supported by specific molecular elements. Main conclusions Dodonaea viscosa is not an old lineage, as has often been speculated based primarily on its vast distribution. It diverged from its most recent common ancestor and subsequently dispersed and established around the world within the last 2 Myr. Two distinct lineages within Dodonaea viscosa, which have been shaped by Quaternary climatic change, have separate dispersal histories. The molecular investigations have identified that, although there are least two evolutionary lineages within the complex, they do not correlate with any distinct morphological subunits. It is proposed that Dodonaea viscosa (including D. biloba and D. procumbens) be recognized as an ochlospecies.