Invasive Alien Species (IAS) threaten biodiversity, ecosystem functions and services, modify landscapes and impose costs to national economies. Management efforts are underway globally to reduce these impacts, but little attention has been paid to optimising the use of the scarce available resources when IAS are impossible to eradicate, and therefore population reduction and containment of their advance are the only feasible solutions.CONTAIN, a three-year multinational project involving partners from Argentina, Brazil, Chile and the UK, started in 2019. It develops and tests, via case study examples, a decision-making toolbox for managing different problematic IAS over large spatial extents. Given that vast areas are invaded, spatial prioritisation of management is necessary, often based on sparse data. In turn, these characteristics imply the need to make the best decisions possible under likely heavy uncertainty.Our decision-support toolbox will integrate the following components:(i) the relevant environmental, social, cultural, and economic impacts, including their spatial distribution;(ii) the spatio-temporal dynamics of the target IAS (focusing on dispersal and population recovery);(iii) the relationship between the abundance of the IAS and its impacts;(iv) economic methods to estimate both benefits and costs to inform the spatial prioritisation of cost-effective interventions.To ensure that our approach is relevant for different contexts in Latin America, we are working with model species having contrasting modes of dispersal, which have large environmental and/or economic impacts, and for which data already exist (invasive pines, privet, wasps, and American mink). We will also model plausible scenarios for data-poor pine and grass species, which impact local people in Argentina, Brazil and Chile.We seek the most effective strategic management actions supported by empirical data on the species’ population dynamics and dispersal that underpin reinvasion, and on intervention costs in a spatial context. Our toolbox serves to identify key uncertainties driving the systems, and especially to highlight gaps where new data would most effectively reduce uncertainty on the best course of action. The problems we are tackling are complex, and we are embedding them in a process of co-operative adaptive management, so that both researchers and managers continually improve their effectiveness by confronting different models to data. Our project is also building research capacity in Latin America by sharing knowledge/information between countries and disciplines (i.e., biological, social and economic), by training early-career researchers through research visits, through our continuous collaboration with other researchers and by training and engaging stakeholders via workshops. Finally, all these activities will establish an international network of researchers, managers and decision-makers. We expect that our lessons learned will be of use in other regions of the world where complex and inherently context-specific realities shape how societies deal with IAS.