||Aim: To determine which morphological characteristics make a fish species a good candidate for introduction and establishment, we tested whether (a) introduced species differ in morphology from non-introduced species (species only existing in native areas and not introduced to new areas) in each donor assemblage (biogeographic realm fauna); (b) within the introduced species, the morphology of established species (self-sustaining introduced species) differs from that of the non-established species; (c) within the established species, those exported out of their native realm have more extreme morphological traits than those translocated within their native realm. Major taxa studied: Freshwater fish. Location: Global. Time period: 1960s-2010s. Methods: We used a global database of freshwater fishes from the six realms. Ten morphological traits were measured on 9,150 species. Principal component analysis was conducted to combine the 10 traits into a multidimensional morphospace. We used permutational multivariate analysis of variance (PERMANOVA) and permutational analysis for the multivariate homogeneity of dispersions (PERMDISP2) to compare the distribution of species groups in the morphospace and Kolmogorov-Smirnov tests to compare their distributions on principal component (PC) axes. Results: The morphology of introduced species differed from that of non-introduced species in all the six biogeographic realms. Among introduced species, established species had more extreme morphological traits than non-established species in most realms. Among established species, exported species had more extreme morphological traits than translocated species. Main conclusions: Morphological differences between introduced and nonintroduced species rely on an anthropogenic trait selection for fisheries and angling, leading to the preference for the introduction of predators with large and laterally compressed bodies. Established introduced species represent a small subset of introduced species morphologies, with these species having more extreme morphological traits, probably making them more efficient in particular habitats than their non-established counterparts. This was particularly marked for fish morphologies adapted to lentic waters. Such a trend was apparent for exported species, which have more extreme traits than translocated species.