Coral reefs have enormous value in terms of biodiversity and the ecosystem goods and services that they provide to hundreds of millions of people around the world. These important ecosystems are facing rapidly increasing pressure from climate change, particularly ocean warming and acidification. A centrally important question is whether reef-building corals and the ecosystems they build will be able to acclimate, adapt, or migrate in response to rapid anthropogenic climate change. This issue is explored in the context of the current environmental change, which is largely unprecedented in rate and scale and which are exceeding the capacity of coral reef ecosystems to maintain their contribution to human well-being through evolutionary and ecological processes. On the balance of evidence, the 'Red Queen' (an analogy previously used by evolutionary biologists) is clearly being 'left in the dust' with evolutionary processes that are largely unable to maintain the status quo of coral reef ecosystems under the current high rates of anthropogenic climate change.