Weather, climate, and climate change are affecting human health, with scientific evidence increasing substantially over the past two decades, but with very limited research from low- and middle-income countries. The health effects of climate change occur mainly because of the consequences of rising temperatures, rising sea levels, and an increase in extreme weather events. These exposures interact with demographic, socio-economic, and environmental factors, as well as access to and the quality of health care, to affect the magnitude and pattern of risks. Health risks are unevenly distributed around the world, and within countries and across population groups. Existing health challenges and inequalities are likely to be exacerbated by climate change. This narrative review provides an overview of the health impacts of weather, climate, and climate change, particularly on vulnerable regions and populations in sub-Saharan Africa and South Asia, and discusses the importance of protecting human health in a changing climate; such measures are critical to reducing poverty and inequality at all scales. Three case summaries from the INDEPTH Health and Demographic Surveillance Systems highlight examples of research that quantified associations between weather and health outcomes. These and comparable surveillance systems can provide critical knowledge to increase resilience and decrease inequalities in an increasingly warming world.