Although invasive alien species have long been recognized as a major threat to nature and people, until now there has been no comprehensive global review of the status, trends, drivers, impacts, management and governance challenges of biological invasions. The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) Thematic Assessment Report on Invasive Alien Speciesand Their Control (hereafter ‘IPBES invasive alien species assessment’) drew on more than 13,000 scientific publications and reports in 15 languages as well as Indigenous and local knowledge on all taxa, ecosystems and regions across the globe. Therefore, it provides unequivocal evidence of the major and growing threat of invasive alien species alongside ambitious but realistic approaches to manage biological invasions. The extent of the threat and impacts has been recognized by the 143 member states of IPBES who approved the summary for policymakers of this assessment. Here, the authors of the IPBES assessment outline the main findings of the IPBES invasive alien species assessment and highlight the urgency to act now.