Sex chromosomes have evolved independently many times across eukaryotes. Despite a considerable body of literature on sex chromosome evolution, the causes and consequences of variation in their formation, degeneration, and turnover remain poorly understood. Chromosomal rearrangements are thought to play an important role in these processes by promoting or extending the suppression of recombination on sex chromosomes. Sex chromosome variation may also contribute to barriers to gene flow, limiting introgression among species. Comparative approaches in groups with sexual system variation can be valuable for understanding these questions. Rumex is a diverse genus of flowering plants harboring significant sexual system and karyotypic variation, including hermaphroditic and dioecious clades with XY (and XYY) sex chromosomes. Previous disagreement in the phylogenetic relationships among key species has rendered the history of sex chromosome evolution uncertain. Resolving this history is important for investigating the interplay of chromosomal rearrangements, introgression, and sex chromosome evolution in the genus. Here, we use new transcriptome assemblies from 11 species representing major clades in the genus, along with a whole-genome assembly generated for a key hermaphroditic species. Using phylogenomic approaches, we find evidence for the independent evolution of sex chromosomes across two major clades, and introgression from unsampled lineages likely predating the formation of sex chromosomes in the genus. Comparative genomic approaches revealed high rates of chromosomal rearrangement, especially in dioecious species, with evidence for a complex origin of the sex chromosomes through multiple chromosomal fusions. However, we found no evidence of elevated rates of fusion on the sex chromosomes in comparison with autosomes, providing no support for an adaptive hypothesis of sex chromosome expansion due to sexually antagonistic selection. Overall, our results highlight a complex history of karyotypic evolution in Rumex, raising questions about the role that chromosomal rearrangements might play in the evolution of large heteromorphic sex chromosomes.