There is concern that the rate of environmental change is now exceeding the capacity of many populations to adapt. Mitigation of biodiversity loss requires science that integrates both ecological and evolutionary responses of populations and communities to rapid environmental change, and can identify the conditions that allow the recovery of declining populations. This special issue focuses on evolutionary rescue (ER), the idea that evolution might occur sufficiently fast to arrest population decline and allow population recovery before extinction ensues. ER emphasizes a shift to a perspective on evolutionary dynamics that focuses on short time-scales, genetic variants of large effects and absolute rather than relative fitness. The contributions in this issue reflect the state of field; the articles address the latest conceptual developments, and report novel theoretical and experimental results. The examples in this issue demonstrate that this burgeoning area of research can inform problems of direct practical concern, such as the conservation of biodiversity, adaptation to climate change and the emergence of infectious disease. The continued development of research on ER will be necessary if we are to understand the extent to which anthropogenic global change will reduce the Earth's biodiversity.