As neglected tropical disease programs look to consolidate the successes of moving towards elimination, we need to understand the dynamics of transmission at low prevalence to inform surveillance strategies for detecting elimination and resurgence. In this special collection, modelling insights are used to highlight drivers of local elimination, evaluate strategies for detecting resurgence, and show the importance of rational spatial sampling schemes for several neglected tropical diseases (specifically schistosomiasis, soil-transmitted helminths, lymphatic filariasis, trachoma, onchocerciasis, visceral leishmaniasis, and gambiense sleeping sickness).