Atmospheric blocking plays an important role in the mid‐latitude climate variability and can be responsible for anomalous mean and/or extreme climate. In this study, a potential vorticity based blocking indicator is used to investigate the representation of Euro‐Atlantic atmospheric blocking events in the ECHAM5/MPI‐OM climate model. The impact of blocking events on present and future mean and extreme climate is studied by means of composite maps and correlation analyses. In comparison to ERA‐40 re‐analysis, the model represents the blocking frequency and seasonal distribution well. We show that European blocking events have a sustained influence particularly on anomalous cold winter temperatures in Europe. In a future climate, the blocking frequency is slightly diminished but the influence on the European winter climate remains robust. Due to a northeastward shift of the blocking pattern and an increase in maximum blocking duration, cold winter temperature extremes can still be expected in a future climate.