Genetic specificity occurs in many host-parasite systems. Each host can recognize and resist only a subset of parasites; each parasite can grow only on particular hosts. Biochemical recognition systems determine which matching host and parasite genotypes result in resistance or disease. Recognition systems are often associated with widespread genetic polymorphism in the host and parasite populations. I describe four systems with matching host-parasite polymorphisms: plant-pathogen interactions, nuclear-cytoplasmic conflict in plants, restriction enzymes in bacterial defence against viruses, and bacterial plasmids that compete by toxin production and toxin immunity. These systems highlight several inductive problems. For example, the observed patterns of resistance and susceptibility between samples of hosts and parasites are often used to study polymorphism. The detectable polymorphism by this method may be a poor guide to the actual polymorphism and to the underlying biochemistry of host-parasite recognition. The problem of using detectable polymorphism to infer the true nature of recognition and polymorphism is exacerbated by non-equilibrium fluctuations in allele frequencies that commonly occur in host-parasite systems. Another problem is that different matching systems may lead either to low frequencies of host resistance and common parasites, or to common resistance and rare parasites. Thus low levels of host resistance or rare parasites do not imply that parasitism is an unimportant evolutionary force on host diversity. Knowledge of biochemical recognition systems and dynamical analysis of models provide a framework for analysing the widespread polymorphisms in host-parasite genetics.