Investors in international agricultural research seek sustainable agri-food technologies that can potentially serve multiple objectives, including economic growth, food security, and sustainable use of natural resources. We employ quantitative economic models to examine the potential multi-dimensional impacts of agricultural productivity gains in the Global South. These models take into account behavior responses to agricultural technological change, i.e., how productivity changes may affect decisions on what to produce, trade, and consume. We consider and compare potential impacts of productivity growth in different technologies and regions and assess implications along several impact dimensions, including economic and income growth, the population at risk of hunger, adequacy of micronutrients in human diets, land and water use, and greenhouse gas emissions. Evidence on the economic significance of major crop and farm animal pests and diseases is also summarized. Potential impacts of technologies that increase agricultural productivity vary widely by commodity, farming system and region. These results can help inform decision-making about an optimal R&D portfolio that takes into account the multiple objectives of agricultural R&D investments and illuminate potential tradeoffs among objectives that may result from different R&D spending decisions.