Abstract A total of 1590 species of arthropods alien to Europe have already established on the continent, including 226 more or less cosmopolitan species of uncertain origin (cryptogenic). These alien species are dispersed across 33 taxonomic orders, including crustaceans, chilopods, diplopods, pauropods, Symphyla, mites, arachnids, and insects. However, insects largely dominate, accounting for more than 87% of the species, far in excess of mites (6.4%). Three of the insect orders, namely Coleoptera, Hemiptera and Hymenoptera, overall account for nearly 65 % of the total. The alien fauna seems to be highly diverse with a total of 257 families involved, of which 30 have no native representatives. However, just 11 families contribute more than 30 species, mainly aphids, scales and hymenopteran chalcids. For a number of families, the arrival of alien species has significantly modified the composition of the fauna in Europe. Examples are given. The number of new records of aliens per year has increased exponentially since the 16th century, but a significant acceleration was observed since the second half of the 20th century, with an average of 19.6 alien species newly reported per year in Europe between 2000 and 2008. This acceleration appears to be mainly related to the arrival of phytophagous species, probably with the plant trade, whereas the contribution of detritivores, parasitoids and predators has decreased. Some taxa have not shown any acceleration in the rate of arrivals. Asia has supplied the largest number of alien arthropods occurring in Europe (26.7 %), followed by North America (21.9%) but large differences in the region of origin are apparent between taxa. Once established, most alien species have not spread throughout Europe, at least yet, with 43.6 % of the species only present in one or two countries, and less than 1% present in more than 40 countries. Large differences also exist between European countries in the total number of alien arthropods recorded per country. Italy (700 species) and France (690 species), followed by Great Britain (533 species), host many more species than other countries. The number of alien species per country is significantly correlated with socioeconomic and demographic variables.