This review discusses the challenges of chemotherapy for human African trypanosomiasis (HAT). The few drugs registered for use against the disease are unsatisfactory for a number of reasons. HAT has two stages. In stage 1 the parasites proliferate in the haemolymphatic system. In stage 2 they invade the central nervous system and brain provoking progressive neurological dysfunction leading to symptoms that include the disrupted sleep wake patterns that give HAT its more common name of sleeping sickness. Targeting drugs to the central nervous system offers many challenges. However, it is the cost of drug development for diseases like HAT, that afflict exclusively people of the world's poorest populations, that has been the principal barrier to new drug development and has led to them becoming neglected. Here we review drugs currently registered for HAT, and also discuss the few compounds progressing through clinical trials. Finally we report on new initiatives that might allow progress to be made in developing new and satisfactory drugs for this terrible disease.