Knowledge of the thermal state of mountain permafrost has greatly increased since 2007 with the establishment of numerous new monitoring stations around the world. Data collected at these sites have pointed to longer-term changes in ground temperatures, which seem to have increased during the last two to three decades in cold permafrost, while in ground close to 0°C the near-surface ice content has restricted warming and similar trends are not apparent. Modelling of mountain permafrost has developed greatly, driven by general circulation models or gridded temperature maps, through both predictive methods and spatial equilibrium and transient approaches. The spatial resolution of climate parameters, which is normally much coarser than the spatial heterogeneity of alpine environments, presents a major problem for modelling studies. This is a fundamental challenge for future research. Copyright © 2013 John Wiley & Sons, Ltd.