The control of neglected tropical diseases (NTDs) has received huge investment in recent years, leading to large reductions in morbidity. In 2012, the World Health Organization set ambitious targets for eliminating many of these diseases as a public health problem by 2020, an aspiration that was supported by donations of treatments, intervention materials, and funding committed by a broad partnership of stakeholders in the London Declaration on NTDs. Alongside these efforts, there has been an increasing role for quantitative analysis and modeling to support the achievement of these goals through evaluation of the likely impact of interventions, the factors that could undermine these achievements, and the role of new diagnostics and treatments in reducing transmission. In this special issue, we aim to summarize those insights in an accessible way. This article acts as an introduction to the special issue, outlining key concepts in NTDs and insights from modeling as we approach 2020., Mathematical modeling has informed the development of control policies for neglected tropical diseases. Here we summarize the insights from a number of studies and the articles included in this issue.