Human African trypanosomiasis (HAT) is a lethal neglected tropical disease (NTD) transmitted by the bite of infected tsetse flies. The disease is also known as “sleeping sickness”. During the 20th century it caused enormous suffering in the endemic areas in sub-Saharan Africa. HAT transmission last soared in the late 1990s, triggering a renewed, coordinated and very successful control effort. In this paper, we present achievements towards HAT elimination, with a focus on the WHO road map targets for 2020. In particular, reported cases continue to decline, from over 30,000 cases per year at the turn of the century to 663 cases in 2020. Despite the impact of the COVID-19 pandemic, HAT surveillance was largely sustained, and the network of health facilities able to diagnose and treat the disease further expanded. Looking to the future, the World Health Organization (WHO) set bold new targets for HAT in its 2021–2030 road map for NTDs, namely: the elimination of transmission of gambiense HAT, which occurs in western and central Africa, and the elimination as a public health problem of rhodesiense HAT, which is found in eastern and southern Africa. The strong commitment of national health authorities and the international community will be essential if these goals are to be achieved.