We survey the current state of a group of parasitic and microbial diseases called the Neglected Tropical Diseases (NTDs). These diseases currently infect a billion people, primarily in socioeconomically depressed areas of the world, are a leading cause of worldwide disability, and are responsible for approximately 534,000 deaths per year. We focus on several subcategories: protozoans, helminthes and bacterial diseases. We identify the populations most at risk from these diseases, and outline symptoms and other disease burdens. We examine the progress being made in controlling NTDs, including the current state of drug development. We also examine mathematical modeling of NTDs. While mathematical modeling is not bound by many of the strictures of access, data collection and infrastructure funding, we nevertheless demonstrate that few NTDs have received much attention from mathematical models, and that some have received no attention at all. Simple mathematical models could contribute significantly to our understanding of these diseases and the efforts required to control them, at very little cost. Further investment in prevention, treatment and awareness of NTDs is urgently warranted.