Aim To explore the biogeographic patterns of exotic species in order to discriminate between hypotheses postulated to produce several biogeographic phenomena: the latitudinal gradient in species richness, the latitudinal gradient in species geographical range size (Rapoport’s rule), species geographical range boundaries and patterns of invasion in the tropics. Location Data were taken from North and South America, Europe, Asia, Africa and oceanic islands. Methods The latitudinal extents of the geographical range of exotic species were recorded to the nearest 1° of latitude from several published sources. Species richness was tabulated by recording the number of naturalized species present within 5° bands of latitude. Rapoport’s rule was calculated by averaging the latitudinal extent of all exotic species present within 5° bands. The low-latitude boundaries of species’ native and naturalized ranges were compared with the nearest 1° of latitude. These comparisons on continents were contrasted with those on islands. Results Within the tropics, few exotic species have become naturalized and those that are have established large geographical ranges. Outside of the tropics, exotic species of birds, mammals, fishes and plants demonstrate qualitatively similar latitudinal gradients in richness and geographical range size. They show the same patterns as native species, where richness is negatively correlated and range size positively correlated with latitude. Further, the geographical ranges of naturalized species on continents rarely extend to latitudes lower than those in their native ranges. On islands (where biotic pressure is reduced) exotic species are more frequently naturalized at latitudes lower than those in their native ranges. Main conclusions Hypotheses for the latitudinal gradient in species richness and geographical range size that are based on past glaciation events or differential rates of speciation between regions may not be necessary to explain these gradients, as exotic species are recent colonists and their patterns of distribution cannot have been directly affected by past glaciation events or differential rates of speciation between regions. Further, the low-latitude boundary of species geographical ranges may be set by tolerance for biotic pressure.