Aim Climate change is expected to drive range shifts among a wide array of organisms. Non-indigenous species (NIS) provide a unique opportunity to observe the establishment of range boundaries in a way that cannot be directly seen for native species. Recent studies have indicated that climate change facilitates biological invasions at local scales. However, the generality of these effects is unclear, as there is a dearth of comparative studies that assess how rapid environmental change affects species ranges across taxa and biogeographic provinces. Location The South African coast and other coastlines across the world. Methods We first studied the distribution of shallow-marine benthic organisms along the South African coastline and analysed the global distribution of NIS. We then obtained DNA sequence data from a suite of co-occurring NIS from along the studied coastline and compared these data with available genetic information from other regions of the world. Subsequently, we conducted physiological experiments to assess how thermal tolerance was related to species distribution. Finally, we analysed ship-based seawater temperature records and compared these with past changes in the range size and abundance of NIS. These records were used to estimate shipping intensity and NIS propagule pressure. Results We found that NIS with a variety of thermal tolerances and distributions have expanded their ranges and increased in abundance as seawater temperature regimes have changed. We found little interannual variation in shipping transport intensity. Most haplotypes of the studied NIS in South Africa were shared with other regions. Main conclusions This study provides empirical evidence that NIS, regardless of their thermal tolerance, range size and genetic variability, are expanding their ranges and increasing in abundance. This trend is uncorrelated with levels of human-mediated NIS transport but concurrent with changes in seawater temperature, which suggests that climate change fosters the spread and abundance of NIS across multiple spatial scales.