We review current ideas about coevolution of plants and parasites, particularly processes that generate genetic diversity. Frequencies of host resistance and parasite virulence alleles that interact in gene-for-gene (GFG) relationships coevolve in the familiar boom-and-bust cycle, in which resistance is selected when virulence is rare, and virulence is selected when resistance is common. The cycle can result in stable polymorphism when diverse ecological and epidemiological factors cause negative direct frequency-dependent selection (ndFDS) on host resistance, parasite virulence, or both, such that the benefit of a trait to fitness declines as its frequency increases. Polymorphism can also be stabilized by overdominance, when heterozygous hosts have greater resistance than homozygotes to diverse pathogens. Genetic diversity can also persist in the form of statistical polymorphism, sustained by random processes acting on gene frequencies and population size. Stable polymorphism allows alleles to be long-lived and genetic variation to be detectable in natural populations. In agriculture, many of the factors promoting stability in host-parasite interactions have been lost, leading to arms races of host defenses and parasite effectors.