The WHO recognizes human African trypanosomiasis, Chagas disease and the leishmaniases as neglected tropical diseases. These diseases are caused by parasitic trypanosomatids and range in severity from mild and self-curing to near invariably fatal. Public health advances have substantially decreased the effect of these diseases in recent decades but alone will not eliminate them. In this Review, we discuss why new drugs against trypanosomatids are required, approaches that are under investigation to develop new drugs and why the drug discovery pipeline remains essentially unfilled. In addition, we consider the important challenges to drug discovery strategies and the new technologies that can address them. The combination of new drugs, new technologies and public health initiatives is essential for the management, and hopefully eventual elimination, of trypanosomatid diseases from the human population.