Evolutionary rescue in a changing world

•Evolutionary rescue can prevent population extinctions.•We synthesize theoretical and experimental studies of evolutionary rescue.•Demographic, genetic, and extrinsic factors influence the probability of evolutionary rescue.•Unequivocal cases of evolutionary rescue in the wild are rare.•We highlight where the field might develop and areas of potential application. Evolutionary rescue occurs when adaptive evolutionary change restores positive growth to declining populations and prevents extinction. Here we outline the diagnostic features of evolutionary rescue and distinguish this phenomenon from demographic and genetic rescue. We then synthesize the rapidly accumulating theoretical and experimental studies of evolutionary rescue, highlighting the demographic, genetic, and extrinsic factors that affect the probability of rescue. By doing so, we clarify the factors to target through management and conservation. Additionally, we identify several putative cases of evolutionary rescue in nature, but conclude that compelling evidence remains elusive. We conclude with a horizon scan of where the field might develop, highlighting areas of potential application, and suggest areas where experimental evaluation will help to evaluate theoretical predictions.