Invasive Alien Species (IAS) are amongst the most significant drivers of species extinction and ecosystem degradation, causing negative impacts on ecosystem services and human well-being. InvasiBES, a project funded by BiodivERsA-Belmont Forum for 2019–2021, will use data and models across scales, habitats and species to understand and anticipate the multi-faceted impacts of IAS and to provide tools for their management. Using Alien Species Narratives as reference, we will design future intervention scenarios focused on prevention, control and eradication of IAS in Europe and the United States, through a participatory process bringing together the expertise of scientists and stakeholders. We will also adapt current impact assessment protocols to assess both the detrimental and beneficial impacts of IAS on biodiversity and ecosystem services. This information will then be combined with maps of the potential distribution of Invasive Species of Interest in Europe under current and future climate-change scenarios. Likewise, we will anticipate areas under risk of invasion by range-shifting plants of concern in the US. Finally, focusing on three local-scale studies that cover a range of habitats (freshwater, terrestrial and marine), invasive species (plants and animals) and ecosystem services (supporting, provisioning, regulating and cultural), we will use empirical field data to quantify the real-world impacts of IAS on biodiversity and ecosystem services and calculate indicators of ecosystem recovery after the invader is removed. Spatial planning tools (InVEST) will be used to evaluate the costs and benefits of species-specific intervention scenarios at the regional scale. Data, models and maps, developed throughout the project, will serve to build scenarios and models of biodiversity and ecosystem services that are relevant to underpin management of IAS at multiple scales.