This research was undertaken in order to understand what factors have been driving stunting reduction in Tanzania over the recent past (2005-2015), and what can further accelerate progress against undernutrition in the near future (2015-2025). Chronic undernutrition in early childhood – often indicated by stunting – has highly detrimental consequences for long-term physical and cognitive development, school attendance and performance, and labor productivity and wages in adulthood. Understanding how countries have been able to successfully reduce stunting prevalence, and how they can accelerate this success in the future, are therefore critically important research questions. During the past decade, Tanzania has experienced rapid change in the nutrition status of children 0-5 years, particularly since 2010. Stunting declining from 44.3% in 2004-05 to 42.0% in 2010, before dropping sharply to 34.4% in 2015-16, a decline of 0.9 percentage points per year. This encouraging trend begs the main research question motivating this paper: what explains this progress? We address this question with a quantitative approach built upon both parametric and non-parametric regression techniques, and a simple linear regression decomposition at means. Previous studies applying this approach in South Asia have demonstrated the paramount importance of improvements in household wealth, parental education, maternal and child health care, and water, sanitation and hygiene (WASH). However, a novel contribution of the study is the consideration of infectious diseases, including malaria and HIV/AIDS: both diseases were very common in 2005, yet both saw dramatic improvements in prevention and treatment efforts in subsequent years. We show that proxies for the prevention/treatment of these diseases account for the largest share of the predicted reduction in stunting over 2005-16, that prevention of both diseases is associated with improvements in early childhood nutrition (suggestive of improvements in birth size and growth in early infancy), and that the apparent effects of these public health efforts are larger in regions where the diseases are more prevalent. In contrast, the apparent effects of household wealth, parental education, maternal and child health care and WASH are more important in explaining stunting reduction among older children.