The paper examines non-linear dynamical phenomena in host-parasite interactions by reference to a series of different problems ranging from the impact on transmission of control measures based on vaccination and chemotherapy, to the effects of immunological responses targeted at different stages in a parasite's life-cycle. Throughout, simple mathematical models are employed to aid in interpretation. Analyses reveal that the influence of a defined control measure on the prevalence or intensity of infection, whether vaccination or drug treatment, is non-linearly related to the magnitude of control effort (as defined by the proportion of individuals vaccinated or treated with a drug). Consideration of the relative merits of gametocyte and sporozoite vaccines against malarial parasites suggests that very high leves of cohort immunization will be required to block transmission in endemic areas, with the former type of vaccine being more effective in reducing transmission for a defined level of coverage and the latter being better with respect to a reduction in morbidity. The inclusion of genetic elements in analyses of the transmission of helminth parasites reveals complex non-linear patterns of change in the abundance of different parasite genotypes under selection pressures imposed by either the host immunological defences or the application of chemotherapeutic agents. When resistance genes are present in parasite populations, the degree to which abundance can be suppressed by chemotherapy depends critically on the frequency and intensity of application, with intermediate values of the former being optimal. A more detailed consideration of the impact of immunological defences on parasite population growth within an individual host, by reference to the erythrocytic cycle of malaria, suggests that the effectiveness of a given immunological response is inversely related to the life-expectancy of the target stage in the parasite's developmental cycle.