Biological invasions are one of the major drivers of biodiversity decline and have been shown to have far-reaching consequences for society and the economy. Preventing the introduction and spread of alien species represents the most effective solution to reducing their impacts on nature and human well-being. However, implementing effective solutions requires a good understanding of where the species are established and how biological invasions develop over time. Knowledge of the status and trends of biological invasions is thus key for guiding research efforts, informing stakeholders and policymakers, for targeted management efforts, and preparing for the future. However, information about the status and trends of alien species is scattered, patchy, and highly incomplete, making it difficult to assess. Published reports for individual regions and taxonomic groups are available, but large-scale overviews are scarce. A global assessment therefore requires a review of available knowledge with careful consideration of sampling and reporting biases. This paper provides a comprehensive global assessment of the status and trends of alien species for major taxonomic groups [Bacteria, Protozoa, Stramenopila, Alveolata, and Rhizaria (SAR), fungi, plants, and animals] for Intergovernmental Panel of Biodiversity and Ecosystem Services (IPBES) regions. The review provides irrefutable evidence that alien species have been introduced to all regions worldwide including Antarctica and have spread to even the most remote islands. The numbers of alien species are increasing within all taxa and across all regions, and are often even accelerating. Large knowledge gaps exist, particularly for taxonomic groups other than vascular plants and vertebrates, for regions in Africa and Central Asia, and for aquatic realms. In fact, for inconspicuous species, such as Bacteria, Protozoa, and to some degree SAR and fungi, we found records for very few species and regions. Observed status and trends are thus highly influenced by research effort. More generally, it is likely that all lists for alien species of any taxonomic group and region are incomplete. The reported species numbers therefore represent minima, and we can expect additions to all lists in the near future. We identified six key challenges which need to be addressed to reduce knowledge gaps and to improve our ability to assess trends and status of biological invasions.