For more than a century Alpine glaciers have been retreating dramatically, and they are expected to shrink even more quickly over the coming decades. This study addresses the future evolution of Grosser Aletschgletscher, Switzerland, the largest glacier in the European Alps. A three-dimensional combined surface mass-balance and glacier dynamics model was applied. The ice flow was described with the full Stokes equations. The glacier surface evolution was obtained by solving a transport equation for the volume of fluid. Daily surface melt and accumulation were calculated on the basis of climate data. The combined model was validated against several types of measurements made throughout the 20th century. For future climate change, scenarios based on regional climate models in the ENSEMBLES project were used. According to the median climatic evolution, Aletschgletscher was expected to lose 90% of its ice volume by the end of 2100. Even when the model was driven using current climate conditions (the past two decades) the glacier tongue experienced a considerable retreat of 6 km, indicating its strong disequilibrium with the present climate. By including a model for the evolution of supraglacial debris and its effect in reducing glacier melt, we show that this factor can significantly slow future glacier retreat.