Climate change and biological invasions are key processes affecting global biodiversity, yet their effects have usually been considered separately. Here, we emphasise that global warming has enabled alien species to expand into regions in which they previously could not survive and reproduce. Based on a review of climate-mediated biological invasions of plants, invertebrates, fishes and birds, we discuss the ways in which climate change influences biological invasions. We emphasise the role of alien species in a more dynamic context of shifting species' ranges and changing communities. Under these circumstances, management practices regarding the occurrence of 'new' species could range from complete eradication to tolerance and even consideration of the 'new' species as an enrichment of local biodiversity and key elements to maintain ecosystem services.