Sunflowers are well-established model organisms in evolutionary biology; studies of them have made important contributions to our understanding of hybridization as an evolutionarily constructive process. Here, after introducing earlier foundational work, we review recent population genomics studies in this group. We discuss the origin of sunflowers, and how genomic data has helped disentangle species relationships. We then review work on past and ongoing speciation, as well as adaptation in natural populations or during domestication and the evolution of invasiveness. Results from these studies have shed light on the nature of sunflower species, revealing that sunflower genomes are mosaics that retain evidence of past and ongoing hybridization with congeners. This occurs even in species for which multiple compounded isolating mechanisms prevent interbreeding. Studies of cultivated sunflowers have similarly clarified that a substantial fraction of the domesticated gene pool is derived from introgressions from as many as half a dozen different species, while also identifying cases of crop-wild gene flow. In invasive species, hybridization may occasionally spur highly competitive genotypes, including in perennial species where the beneficial effects of hybrid vigor can be maintained. Population genomics studies have shown that large chromosomal blocks of high linkage disequilibrium, many of which are chromosomal inversions, facilitate local adaptation of sunflower populations given widespread gene flow. These haploblocks were found to control multiple traits and are often themselves the result of hybridization and introgression. We conclude by considering future research challenges for the sunflower community. These include a thorough characterization of sunflower structural variation and the generation of new reference genomes, revisiting earlier studies based on non-genomic data, and the optimization of transformation methods that can be used to validate the function of ecologically or economically important genes.