The thermal tropopause, which marks the transition between the troposphere below and the stratosphere above, is a key indicator of the thermal structure of the upper troposphere and lower stratosphere (UTLS), and changes in tropopause structure are closely linked to changes in atmospheric circulation. Here, we analyze climate model simulations from two model intercomparison projects (CCMI–2022, CMIP6) and from targeted simulation experiments with the ECHAM MESSy Atmospheric Chemistry model (EMAC) and compare to ERA5 reanalysis and satellite observations. Consistent with previous analyses we find that climate models systematically place the extratropical thermal tropopause too high, yielding tropopause pressures lower than observed. These tropopause biases are associated with a cold bias in the lowermost stratosphere, which itself appears to be related to a moist bias in this region. In particular, the sensitivity of extratropical tropopause pressure to changes in water vapour mixing ratios in the lowermost stratosphere (LMS) estimated from multi-model statistics agrees well with the sensitivity predicted from the targeted simulation experiments. Seasonal and inter-annual variability in the pressure level of the extratropical tropopause is found to be slightly underestimated in the model simulations, while trends over past decades show a stronger tropopause rise in models than in the reanalysis. Model projections of future tropopause trends depend strongly on the emission scenario and show substantial spread between the different climate models. We conclude that addressing moist biases in the lowermost stratosphere is essential for reliable simulation of the thermal structure of the UTLS and the tropopause in climate models.