Many hermaphroditic plants avoid self-fertilization by rejecting pollen that express genetically-determined specificities in common with the pistil. Self-incompatibility systems typically show extremely high genetic diversity, some maintaining hundreds of specificities. This article addresses the genetic and evolutionary mechanisms through which new mating specificities arise. Recent investigations of the genetic and physiological basis of self-incompatibility are reviewed. Two evolutionary pathways are considered: one which requires full expression of self-incompatibility in all intermediates and one in which new mating specificities arise through episodes of partial breakdown and restoration of self-incompatibility.