The data needed to develop analytical models of trypanosomiasis transmission have become available only recently. By making some simplifying assumptions, models of the dynamics of the disease in vector, cattle and wild mammal populations can be constructed in order to determine criteria for successful disease control by mass and targetted chemotherapy, and by vector control. The heterogeneity in transmission due to tsetse fly feeding preferences and the variability of immunological characteristics among the vertebrate hosts account for differences in prevalence of Trypanosoma vivax and T. congolense, and also lead to an increase in the basic reproductive rates of the parasites and a corresponding decrease in the vector population density threshold for disease eradication or persistence. The long life-span of the vectors relative to the duration of the parasites' developmental period lead to high infection rates in the vector and high values of R0. The efficacy of chemotherapeutic regimes depends on the relationship between treatment rate and the duration of prophylaxis conferred by the drugs used. The model's predictions of the effects of vector control are shown to be in broad agreement with published field data for Mkwaja Ranch, Tanzania. Vector control programmes are frequently blighted by reinvasion, and the implications of this are discussed in terms of a model for fly immigration. With immigration of vectors, the disease is always endemic, though the infection rate in the fly population is modified by the effect of differential mortalities inside and outside the controlled area on cohorts of incubating flies. Sensitivity analysis of the model, using Monte-Carlo methods, enables an assessment of the relative importance of the parameters to be made. The results emphasize the need for studies of the wild animal reservoir to be carried out alongside entomological surveys. The relative accuracy with which field measurements need to be made in order to minimize the uncertainty in predictions of trypanosomiasis prevalence is discussed.