Understanding how crop plants evolved from their wild relatives and spread around the world can inform about the origins of agriculture. Here, we review how the rapid development of genomic resources and tools has made it possible to conduct genetic mapping and population genetic studies to unravel the molecular underpinnings of domestication and crop evolution in diverse crop species. We propose three future avenues for the study of crop evolution: establishment of high-quality reference genomes for crops and their wild relatives; genomic characterization of germplasm collections; and the adoption of novel methodologies such as archaeogenetics, epigenomics, and genome editing.