With the Paris Agreement, the urgency of limiting ongoing anthropogenic climate change has been recognised. More recent discussions have focused on the difference of limiting the increase in global average temperatures below 1.0, 1.5, or 2.0g C compared to preindustrial levels. Here, we assess the impacts that such different scenarios would have on both the future evolution of glaciers in the European Alps and the water resources they provide. Our results show that even half-degree differences in global temperature targets have important implications for the changes predicted until 2100, and that-for the most optimistic scenarios-glaciers might start to partially recover, owing to possibly decreasing temperatures after the end of the 21st century.