Determining the spread and potential geographical distribution of invasive species is integral to making invasion biology a predictive science. We assembled a dataset of over 1000 occurrences of the Argentine ant (Linepithema humile), one of the world's worst invasive alien species. Native to central South America, Argentine ants are now found in many Mediterranean and subtropical climates around the world. We used this dataset to assess the species' potential geographical and ecological distribution, and to examine changes in its distributional potential associated with global climate change, using techniques for ecological niche modelling. Models developed were highly predictive of the species' overall range, including both the native distributional area and invaded areas worldwide. Despite its already widespread occurrence, L. humile has potential for further spread, with tropical coastal Africa and southeast Asia apparently vulnerable to invasion. Projecting ecological niche models onto four general circulation model scenarios of future (2050s) climates provided scenarios of the species' potential for distributional expansion with warming climates: generally, the species was predicted to retract its range in tropical regions, but to expand at higher latitude areas.