A major issue in ecology, biogeography, conservation biology and invasion biology is the extent to which climate, and hence climate change, contributes to the positions of species' range boundaries. Thirty years of rapid climate warming provides an excellent opportunity to test the hypothesis that climate acts as a major constraint on range boundaries, treating anthropogenic climate change as a large-scale experiment. UK and global data, and literature. This article analyses the frequencies with which species have responded to climate change by shifting their range boundaries. It does not consider abundance or other changes. For the majority of species, boundaries shifted in a direction that is concordant with being a response to climate change; 84% of all species have expanded in a polewards direction as the climate has warmed (for the best data available), which represents an excess of 68% of species after taking account of the fact that some species may shift in this direction for non-climatic reasons. Other data sets also show an excess of animal range boundaries expanding in the expected direction. Climate is likely to contribute to the majority of terrestrial and freshwater range boundaries. This generalization excludes species that are endemic to specific islands, lakes, rivers and geological outcrops, although these local endemics are not immune from the effects of climate change. The observed shifts associated with recent climate change are likely to have been brought about through both direct and indirect (changes to species' interactions) effects of climate; indirect effects are discussed in relation to laboratory experiments and invasive species. Recent observations of range boundary shifts are consistent with the hypothesis that climate contributes to, but is not the sole determinant of, the position of the range boundaries of the majority of terrestrial animal species.