Breeding systems are important, and often neglected, aspects of the natural biology of organisms, affecting homozygosity and thus many aspects of their biology, including levels and patterns of genetic diversity and genome evolution. Among the different plant mating systems, it is useful to distinguish two types of systems: 'sex systems', hermaphroditic versus male/female and other situations; and the 'mating systems' of hermaphroditic populations, inbreeding, outcrossing or intermediate. Evolutionary changes in breeding systems occur between closely related species, and some changes occur more often than others. Understanding why such changes occur requires combined genetical and ecological approaches. I review the ideas of some of the most important theoretical models, showing how these are based on individual selection using genetic principles to ask whether alleles affecting plants' outcrossing rates or sex morphs will spread in populations. After discussing how the conclusions are affected by some of the many relevant ecological factors, I relate these theoretical ideas to empirical data from some of the many recent breeding system studies in plant populations.