In 2012 human African trypanosomiasis (HAT), also known as sleeping sickness, was targeted for elimination as a public health problem, set to be achieved by 2020. The World Health Organization (WHO) provides here the 2018 update on the progress made toward that objective. Global indicators are reviewed, in particular the number of reported cases and the areas at risk. Recently developed indicators for the validation of HAT elimination at the national level are also presented. With 977 cases reported in 2018, down from 2,164 in 2016, the main global indicator of elimination is already well within the 2020 target (i.e. 2,000 cases). Areas at moderate or higher risk (i.e. ≥ 1 case/10,000 people/year) are also steadily shrinking (less than 200,000 km2 in the period 2014-2018), thus nearing the 2020 target i.e. 90% reduction (638,000 km2) from the 2000-2004 baseline (709,000 km2). Health facilities providing diagnosis and treatment of gambiense HAT continued to increase (+7% since the previous survey), with a better coverage of at-risk populations. By contrast, rhodesiense HAT health facilities decreased in number (-10.5%) and coverage. At the national level, eight countries meet the requirements to request validation of gambiense HAT elimination as a public health problem (i.e. Benin, Burkina Faso, Cameroon, Côte d'Ivoire, Ghana, Mali, Rwanda, and Togo), while for other endemic countries more efforts are needed in surveillance, control, or both. The 2020 goal of HAT elimination as a public health problem is within grasp, and eligible countries are encouraged to request validation of their elimination status. Beyond 2020, the HAT community must gear up for the elimination of gambiense HAT transmission (2030 goal), by preparing for both the expected challenges (e.g. funding, coordination, integration of HAT control into regular health systems, development of more adapted tools, cryptic trypanosome reservoirs, etc.) and the unexpected ones.