Projected future climate change will alter carbon storage in forests, which is of pivotal importance for the national carbon balance of most countries. Yet, national-scale assessments are largely lacking. We evaluated climate impacts on vegetation and soil carbon storage for Swiss forests using a dynamic vegetation model. We considered three novel climate scenarios, each featuring a quantification of the inherent uncertainty of the underlying climate models. We evaluated which regions of Switzerland would benefit or lose in terms of carbon storage under different climates, and which abiotic factors determine these patterns. The simulation results showed that the prospective carbon storage ability of forests depends on the current climate, the severity of the change, and the time required for new species to establish. Regions already prone to drought and heat waves under current climate will likely experience a decrease in carbon stocks under prospective 'extreme' climate change, while carbon storage in forests close to the upper treeline will increase markedly. Interestingly, when climate change is severe, species shifts can result in increases in carbon stocks, but when there is only slight climate change, climate conditions may reduce growth of extant species while not allowing for species shifts, thus leading to decreases in carbon stocks.