Invasive species pose the greatest threat to biodiversity, having a significant impact on the native biota and ecosystems. With the added challenge of climate change, it remains uncertain how these invasive mammals will spread globally in the future. Using species distribution modelling, we assessed the potential distribution of 64 invasive mammals and identified hotspots of invasion. Our findings indicate that European countries are particularly vulnerable to mammal invasions. Our analysis of niche dynamics also suggests that 37 out of 64 invasive mammals are experiencing niche shifts, which could portend future invasions.