The paleontological record of mammals offers many examples of evolutionary change, which are well documented at many levels of the biological hierarchy-at the level of species (and above), populations, morphology, and, in ideal cases, even genes. The evolutionary changes developed against, backdrop of climatic change that took place on different scales, from rapid shifts in climate state that took only a few decades, to those that occurred over a millennial scale, to regular glacial-interglacial transitions with cycles of roughly a hundred thousand years, to long-term warming or cooling trends over hundreds of thousands to millions of years. Are there certain scales of climatic change that accelerate evolution? And what will the current global warming event do to evolutionary rates? Here we use paleontology-the study of fossils-to illustrate the scientific method behind answering such complex questions, and to suggest that current rates of global warming are far too fast to influence evolution much and instead are likely to accelerate extinctions.