As the climate continues to change, species are moving to track their historical niches. Although we are gaining a clearer picture of where and how quickly species ranges are moving, a mechanistic understanding of these changes is still nascent. Evolutionary changes in ranges and range-limiting traits over contemporary timescales has received relatively little attention, possibly due to the mismatch in scale between rapid contemporary range shifts and the historical evolution of species ranges over millions of years. But recent experimental work has shown that range-limiting traits can evolve rapidly over decadal timescales, effectively putting evolution back on the table towards the goal of a mechanistic understanding of contemporary range shifts. Here I review the role of evolution in shaping range shift responses to recent climate change from the perspective of the past (shared evolutionary history, or phylogenetic signal in range shifts and range-limiting traits), present (variation in range-limiting traits), and future (incorporating evolution of range-limiting traits into range forecasts from species distribution models). In each of these areas, I found a critical role for evolution in understanding historical constraints and future changes in species ranges over contemporary timescales: shared evolutionary history may constrain range shift responses for some taxa; compensatory mechanisms of phenotypic plasticity and adaptive evolution can modulate the range shift response; and incorporating evolution into species distribution models can qualitatively alter forecasts of future range shifts. Yet, more can be done in this context, and so I conclude by outlining near- and long-term goals for improving our understanding of the role of evolution in shaping species ranges in a rapidly changing world.