We investigate the statistics and dynamics of extreme heat waves over different areas of Europe. We find heatwaves over France and Scandinavia to be associated with recurrent wavenumber three teleconnection patterns in surface temperature and mid-tropospheric geopotential height. For heatwaves with return times of 4 years these teleconnection patterns and their dynamics are robustly represented in a hierarchy of models of different complexity and in reanalysis data. For longer return times, reanalysis records are too short to give statistically significant results, while models confirm the relevance of these large scale patterns for the most extreme heatwaves. A time series analysis shows that heatwave indices defined at synoptic scale are fairly well described by Gaussian stochastic processes, and that these Gaussian processes reproduce well return time plots even for very rare events. These results suggest that extreme heatwaves over different areas of Europe show recurrent typical behaviours in terms of long-range spatial correlations and subseasonal-scale temporal correlations. These properties are consistently represented among models of different complexity and observations, thus suggesting their relevance for a better understanding of the drivers and causes of the occurrence of extreme midlatitude heatwaves and their predictability.