Adaptations to the cold and to short growing seasons characterize arctic life, but climate in the Arctic is warming at an unprecedented rate. Will plant and animal populations of the Arctic be able to cope with these drastic changes in environmental conditions? Here we explore the potential contribution of evolution by natural selection to the current response of populations to climate change. We focus on the spring phenology of populations because it is highly responsive to climate change and easy to document across a wide range of species. We show that evolution can be fast and can occur at the time scale of a few decades. We present an example of reproductive phenological change associated with climate change (North American red squirrels in the Yukon), where a detailed analysis of quantitative genetic parameters demonstrates contemporary evolution. We answer a series of frequently asked questions that should help biologists less familiar with evolutionary theory and quantitative genetic methods to think about the role of evolution in current responses of ecological systems to climate change. Our conclusion is that evolution by natural selection is a pertinent force to consider even at the time scale of contemporary climate changes. However, all species may not be equal in their capacity to benefit from contemporary evolution.