Invasive alien species pose a major threat to biodiversity and natural ecosystems globally and negatively affect conservation efforts in protected areas. They can negatively alter biodiversity and ecological regimes and are a financial burden. Because of their negative impacts, it is important to better understand the threat and management of invasive alien species in protected areas (PAs) globally, and to know how these factors have changed over time. We give an update and compare how the threat and management of invasive species has changed in 21 PAs that were analysed as part of the international SCOPE programme on biological invasions in the mid-1980s. Of all the taxa analysed, invasive plants pose the greatest continued threat, and their numbers have increased in 31% of the PAs. Conversely, mammal invasions now represent less of a threat due to effective management in many PAs; 43% of PAs show a decrease in listed invasive alien mammal taxa. Invasions of amphibians, reptiles, and fish have remained stable over the three decades; around half of the PAs show no change for these taxa. Managers of most PAs consider the threat of invasions to be increasing, despite many (55%) PAs having sustained long-term management programmes and 45% having implemented additional ad hoc approaches. We draw on lessons from this analysis to support the future management of biological invasions in conservation areas. In particular, better monitoring and collation of data is needed, followed by increased preventative measures and the promotion of biological control for widespread species. [link to publication]