We show how directly transmitted microparasites, broadly defined to include viruses, bacteria, protozoans and fungi, may regulate natural populations of invertebrate hosts. The study combines elements of conventional epidemiology (where the host population is assumed constant) with elements of prey-predator studies (which conventionally emphasize how prey and predator populations may be regulated by their interaction). To this end, we construct simple models embodying the essentials of the dynamical interaction between invertebrate hosts and their directly transmitted microparasites. In successive refinements, these models include the effects of recovery and disease-induced mortality, castration or diminished reproduction of infected hosts, vertical transmission, latent periods of infection, stress-related pathogenicity, the interplay between disease and other density-dependent constraints on host population growth, and free-living infective stages. In analysing the dynamical behaviour of these models, we focus on: the possible regulation of the host population by the parasite; the basic reproductive rate of the parasite, and the way in which it affects the dynamics and the evolution of the host-parasite association; and the threshold host density and its implications for endemic or epidemic maintenance of the infection. These are examined in the light of synoptic compilations of field and laboratory data on: birth rates (and disease-induced reduction thereof), natural death rates and disease-induced death rates of hosts; latent periods and efficiencies of vertical transmission of pathogens; the rate of production and lifetime of free-living infective stages; and some characteristics of long-term cycles and of epidemic outbreaks of disease in forest insects. In particular, our models suggest that the baculovirus and microsporidian infections of many temperate forest insects will tend to produce stable cycles in host abundance and in prevalence of infection, with periods in the range 5-12 years. Enough is known about the European larch budmoth and an associated granulosis virus for us to undertake a detailed comparison between theory and data that strongly suggests that the observed 9-10 year cycles are driven by the host-parasite interaction. We also discuss the possible control of invertebrate pest species by pathogens, showing how our models could guide laboratory or field studies, to help estimate whether a given pathogen is capable of regulating the target pest population, and, if so, roughly what quantity is needed to effect a specific level of (local) control. Throughout, the emphasis is on the biological ingredients of the models, and on the biological conclusions to be drawn; mathematical details are given in appendixes.