There is a growing appreciation that chromosome inversions affect rates of adaptation, speciation, and the evolution of sex chromosomes. Comparative genomic studies have identified many new paracentric inversion polymorphisms. Population models suggest that inversions can spread by reducing recombination between alleles that independently increase fitness, without epistasis or coadaptation. Areas of linkage disequilibrium extend across large inversions but may be interspersed by areas with little disequilibrium. Genes located within inversions are associated with a variety of traits including those involved in climatic adaptation. Inversion polymorphisms may contribute to speciation by generating underdominance owing to inviable gametes, but an alternative view gaining support is that inversions facilitate speciation by reducing recombination, protecting genomic regions from introgression. Likewise, inversions may facilitate the evolution of sex chromosomes by reducing recombination between sex determining alleles and alleles with sex-specific effects. However, few genes within inversions responsible for fitness effects or speciation have been identified.