Climate change is projected to increase hydropower generation in some parts of the world and decrease it in others. Here we explore the possible consequences of these impacts for the electricity supply sector at the global scale. Regional hydropower projections are developed by forcing a coupled global hydrological and dam model with downscaled, bias-corrected climate realizations. Consequent impacts on power sector composition and associated emissions and investment costs are explored using the Global Change Assessment Model (GCAM). We find that climate-driven changes in hydropower generation may shift power demands onto and away from carbon intensive technologies. This causes significantly altered power sector CO2 emissions in several hydro-dependent regions, although the net global impact is modest. For drying regions, we estimate a global, cumulative investment need of approximately one trillion dollars (±$500 billion) this century to make up for deteriorated hydropower generation caused by climate change. Total investments avoided are of a similar magnitude across regions projected to experience increased precipitation. Investment risks and opportunities are concentrated in hydro-dependent countries for which significant climate change is expected. Various countries throughout the Balkans, Latin America and Southern Africa are most vulnerable, whilst Norway, Canada, and Bhutan emerge as clear beneficiaries.