Invasive alien species come from most taxonomic groups, and invasion biology is searching for robust cross-taxon generalizations and principles. An analysis of 2,670 papers dealing with 892 invasive species showed that all major groups of invaders are well studied, but that most information on the mechanisms of invasion has emerged from work on a limited number of the most harmful invaders. A strong geographical bias, with Africa and Asia understudied, inhibits a balanced understanding of invasion, because we might be lacking knowledge of specific invasion mechanisms from poorly studied, regionally specific habitats. International cooperation is required to achieve a more geographically balanced picture of biological invasions. Invasive species with the greatest impact are best studied, but more studies of species that are naturalized but not (yet) invasive are needed to improve understanding of the mechanisms acting during the naturalization phase of invasions and leading to successful invasion.