Earth's climate is dynamic, with strong glacial-interglacial cycles through the Late Quaternary. These climate changes have had major consequences for the distributions of species through time, and may have produced historical legacies in modern ecological patterns. Unstable regions are expected to contain few endemic species, many species with strong dispersal abilities, and to be susceptible to the establishment of exotic species from relatively stable regions. We test these hypotheses with a global dataset of grass species distributions. We described global patterns of endemism, variation in the potential for rapid population spread, and exotic establishment in grasses. We then examined relationships of these response variables to a suite of predictor variables describing the mean, seasonality and spatial pattern of current climate and the temperature change velocity from the Last Glacial Maximum to the present. Grass endemism is strongly concentrated in regions with historically stable climates. It also depends on the spatial pattern of current climate, with many endemic species in areas with regionally unusual climates. There was no association between the proportion of annual species (representing potential population spread rates) and climate change velocity. Rather, the proportion of annual species depended very strongly on current temperature. Among relatively stable regions (<10 m year ), increasing velocity decreased the proportion of species that were exotic, but this pattern reversed for higher-velocity regions (>10 m year ). Exotic species were most likely to originate from relatively stable regions with climates similar to those found in their exotic range. Long-term climate stability has important influences on global endemism patterns, largely confirming previous work from other groups. Less well recognized is its role in generating patterns of exotic species establishment. This result provides an important historical context for the conjecture that climate change in the near future may promote species invasions.