Human-mediated transport beyond biogeographic barriers has led to the introduction and establishment of alien species in new regions worldwide. However, we lack a global picture of established alien species richness for multiple taxonomic groups. Here, we assess global patterns and potential drivers of established alien species richness across eight taxonomic groups (amphibians, ants, birds, freshwater fishes, mammals, vascular plants, reptiles and spiders) for 186 islands and 423 mainland regions. Hotspots of established alien species richness are predominantly island and coastal mainland regions. Regions with greater gross domestic product per capita, human population density, and area have higher established alien richness, with strongest effects emerging for islands. Ants and reptiles, birds and mammals, and vascular plants and spiders form pairs of taxonomic groups with the highest spatial congruence in established alien richness, but drivers explaining richness differ between the taxa in each pair. Across all taxonomic groups, our results highlight the need to prioritize prevention of further alien species introductions to island and coastal mainland regions globally.