The health risks of heat exposure depend strongly on relative humidity (RH), as high RH prevents evaporation and thus blocks the evaporative heat loss that gives perspiration its cooling effect. The close connection between RH and heat stress means that changes in RH matter the most in climates that are already hot and humid, including the global tropics and subtropical maritime regions like Florida. These climates are home to much of the world's population, thus RH change in a changing climate is a question of great practical importance. But climate models do not produce consistent results for RH change and the basic science of RH change is not yet adequate to provide much guidance. A case in point is India, where RH has increased by 5-10% since the 1970s, in opposition to the decline in continental RH with warmer temperatures expected from theoretical arguments. Work funded here seeks to develop a theoretical framework for ground-level RH over tropical continents that can account for changes over the past 50 years and provide an estimate for the RH change that is likely to occur as the tropics continue to warm. The work is based on a budget equation in which RH variations are ascribed to changes in atmospheric transport of moisture from adjacent oceans, vertical mixing of moisture by atmospheric convection, and transfer of heat and moisture between the atmosphere and the land below it. The theory is distinctly tropical as it assumes that onshore moisture transport