The geographical exchange of non-native species can be highly asymmetrical, with some world regions donating or receiving more species than others. Several hypotheses have been proposed to explain such asymmetries, including differences in propagule pressure, source species (invader) pools, environmental features in recipient regions, or biological traits of invaders. We quantified spatiotemporal patterns in the exchange of non-native insects between Europe, North America, and Australasia, and then tested possible explanations for these patterns based on regional trade (import values) and model estimates of invader pool sizes. Europe was the dominant donor of non-native insect species between the three regions, with most of this asymmetry arising prior to 1950. This could not be explained by differences in import values (1827–2014), nor were there substantial differences in the sizes of modelled invader pools. Based on additional evidence from literature, we propose that patterns of historical plant introductions may explain these asymmetries, but this possibility requires further study.