Pathogenic animal trypanosomes affecting livestock have represented a major constraint to agricultural development in Africa for centuries, and their negative economic impact is increasing in South America and Asia. Chemotherapy and chemoprophylaxis represent the main means of control. However, research into new trypanocides has remained inadequate for decades, leading to a situation where the few compounds available are losing efficacy due to the emergence of drug-resistant parasites. In this review, we provide a comprehensive overview of the current options available for the treatment and prophylaxis of the animal trypanosomiases, with a special focus on the problem of resistance. The key issues surrounding the main economically important animal trypanosome species and the diseases they cause are also presented. As new investment becomes available to develop improved tools to control the animal trypanosomiases, we stress that efforts should be directed towards a better understanding of the biology of the relevant parasite species and strains, to identify new drug targets and interrogate resistance mechanisms.