Biodiversity and ecosystem services are considered global public goods as they provide, among others, a wide range of material benefits for humanity such as air, water, and nutrients, or immaterial ones such as spiritual fulfilment, aesthetic pleasure, and recreation. However, their continued degradation has led to more poverty, conflict, and displacement. Factors such as habitat destruction, pollution, unsustainable exploitation of resources, climate change, and the proliferation of invasive alien species (IAS) have strongly threatened the planet’s biodiversity. Founded in Panama in 2012 by the Food and Agriculture Organization of the United Nations (FAO) and the Convention on Biological Diversity (CBD), the Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES) has become an independent global reference that has provided rigorous scientific assessments of the state of ecosystems at a global level. In this sense, IPBES recently presented (Sept. 2023) the first global assessment of the impacts of (IAS), revealing that there are more than 18,000 species considered invasive worldwide and that they are present on all continents except Antarctica, having already caused the extinction of more than 500 native species of plants and animals and causing an estimated cost of between 300 and 500 billion euros. Based on critical discourse analysis and applying a specific lens from environmental anthropology, the main objective of this chapter is to understand how the concepts of invasiveness and alienness are presented in this report, also focusing on the idea of the futurity of public policies, questioning whether if “we still have time”?