Midlatitude atmospheric blocking anticyclones (blockings) are related to long lasting severe weather events, such as extreme temperatures and drought. Consequently, they play a major role in midlatitude climate variability. Until recently, global climate models underestimated the frequency and persistence of these blockings, a bias that can be eradicated by increasing the horizontal resolution of the models. We will study the role of horizontal resolution in a new generation of climate models to enhance understanding of the dynamics that are associated with blocking, in simulations and in the actual atmosphere. We will subsequently make process-based projections of Euro-Atlantic blocking for the next decades.