Animal trypanosomiasis (AT) is a complex of veterinary diseases known under various names such as nagana, surra, dourine and mal de caderas, depending on the country, the infecting trypanosome species and the host. AT is caused by parasites of the genus Trypanosoma, and the main species infecting domesticated animals are T. brucei brucei, T. b. rhodesiense, T. congolense, T. vivax, T. evansi and T. equiperdum. AT transmission, again depending on species, is through tsetse flies or common Stomoxys and tabanid flies or through copulation. Therefore, the geographical spread of all forms of AT together is not restricted to the habitat of a single vector like the tsetse fly and currently includes almost all of Africa, and most of South America and Asia. The disease is a threat to millions of companion and farm animals in these regions, creating a financial burden in the billions of dollars to developing economies as well as serious impacts on livestock rearing and food production. Despite the scale of these impacts, control of AT is neglected and under-resourced, with diagnosis and treatments being woefully inadequate and not improving for decades. As a result, neither the incidence of the disease, nor the effectiveness of treatment is documented in most endemic countries, although it is clear that there are serious issues of resistance to the few old drugs that are available. In this review we particularly look at the drugs, their application to the various forms of AT, and their mechanisms of action and resistance. We also discuss the spread of veterinary trypanocide resistance and its drivers, and highlight current and future strategies to combat it.