Aim Recent studies of plant invasions in habitat types across different climatic regions of Europe have made it possible to produce a European map of plant invasions. Parallel research led to the formulation of integrated scenarios of future socio-economic development, which were used to create spatially explicit scenarios of European land-use change for the 21st century. Here we integrate these two research lines and produce the first spatially explicit projections of plant invasions in Europe for the years 2020, 2050 and 2080. Location The European Union (except Bulgaria and Romania), Norway and Switzerland. Methods We used vegetation plots from southern, central and north-western Europe to quantify mean levels of invasion by neophytes (post-1500 alien plants) for forest, grassland, urban, arable and abandoned land. We projected these values on the land-use scenarios for 2020, 2050 and 2080, and constructed maps of future plant invasions under three socio-economic scenarios assuming: (1) deregulation and globalization, (2) continuation of current policies with standing regulations, and (3) a shift towards sustainable development. Results Under all scenarios an increase in the level of invasion was projected for north-western and northern Europe, and under the first two scenarios a decrease for some agricultural areas of eastern Europe where abandonment of agricultural land is expected. A net increase in the level of invasion over Europe was projected under scenarios 2 and 3. Main conclusions The polarization between more and less invaded regions is likely to increase if future policies are oriented on economic deregulation, which may result in serious future problems in some areas of Europe. However, an implementation of sustainability policies would not automatically restrict the spread of alien plants. Therefore invasions require specific policy approaches beyond the more general ones, which are currently on the policy agenda and were tested in the scenarios.