The disciplines of evolutionary biology and plant and animal breeding have been intertwined throughout their development, with responses to artificial selection yielding insights into the action of natural selection and evolutionary biology providing statistical and conceptual guidance for modern breeding. Here we offer an evolutionary perspective on a grand challenge of the 21st century: feeding humanity in the face of climate change. We first highlight promising strategies currently under way to adapt crops to current and future climate change. These include methods to match crop varieties with current and predicted environments and to optimize breeding goals, management practices, and crop microbiomes to enhance yield and sustainable production. We also describe the promise of crop wild relatives and recent technological innovations such as speed breeding, genomic selection, and genome editing for improving environmental resilience of existing crop varieties or for developing new crops. Next, we discuss how methods and theory from evolutionary biology can enhance these existing strategies and suggest novel approaches. We focus initially on methods for reconstructing the evolutionary history of crops and their pests and symbionts, because such historical information provides an overall framework for crop-improvement efforts. We then describe how evolutionary approaches can be used to detect and mitigate the accumulation of deleterious mutations in crop genomes, identify alleles and mutations that underlie adaptation (and maladaptation) to agricultural environments, mitigate evolutionary trade-offs, and improve critical proteins. Continuing feedback between the evolution and crop biology communities will ensure optimal design of strategies for adapting crops to climate change.