Invasions by alien species are one of the major threats to the native environment. There are multifold attempts to counter alien species, but limited resources for mitigation or eradication programmes makes prioritisation indispensable. We used the generic impact scoring system to assess the impact of alien fish species in Europe. It prioritises species, but also offers the possibility to compare the impact of alien invasive species between different taxonomic groups. For alien fish in Europe, we compiled a list of 40 established species. By literature research, we assessed the environmental impact (through herbivory, predation, competition, disease transmission, hybridisation and ecosystem alteration) and economic impact (on agriculture, animal production, forestry, human infrastructure, human health and human social life) of each species. The goldfish/gibel complex Carassius auratus/C. gibelio scored the highest impact points, followed by the grass carp Ctenopharyngodon idella and the topmouth gudgeon Pseudorasbora parva. According to our analyses, alien fish species have the strongest impact on the environment through predation, followed by competition with native species. Besides negatively affecting animal production (mainly in aquaculture), alien fish have no pronounced economic impact. At the species level, C. auratus/C. gibelio show similar impact scores to the worst alien mammals in Europe. This study indicates that the generic impact scoring system is useful to investigate the impact of alien fish, also allowing cross‐taxa comparisons. Our results are therefore of major relevance for stakeholders and decision‐makers involved in management and eradication of alien fish species.