Description: Potential vorticity (PV) cutoffs are stratospheric air masses separated from the circumpolar stratospheric reservoir on an isentropic surface. They typically form via Rossby wave breaking and can strongly influence midlatitude weather; however, the processes governing their evolution are not fully understood. A detailed analysis of two exceptionally long-lived PV cutoffs over Europe is presented to identify the main dynamical and physical processes during their life-cycle. To this end, operational analyses from the European Centre for Medium Range Weather Forecasts (ECMWF) are used together with the cloud top height product from EUMETSAT (European Organisation for the Exploitation of Meteorological Satellites). A combination of Eulerian and Lagrangian diagnostics reveals a complex temporal evolution of the intensity and vertical structure of the two PV cutoffs. They diabatically decay or reappear on lower isentropes and, at the same time, intensify or become reabsorbed by the stratospheric reservoir on higher isentropes. This complex three-dimensional evolution is influenced by a combination of direct and indirect diabatic effects. Convective latent heating, long-wave radiative cooling, and turbulent entrainment of overshooting clouds can all directly modify PV of the cutoff air parcels (direct diabatic effects). In addition, if the cutoff is located in a region with sufficient baroclinicity and low-level moisture, it can contribute to large-scale diabatic ascent, similar to warm conveyor belts in classical extratropical cyclones. The divergent wind and the anticyclonic circulation associated with the low-PV outflow in the upper troposphere can lead to deformation and filamentation of the PV cutoff (indirect diabatic effects). This study extends our understanding of PV cutoffs by (i) emphasising their intricate vertical structure and temporal evolution, (ii) revealing the complex interplay of diabatic processes and how they contribute to the decay and intensification of cutoffs, and (iii) indicating the challenge in correctly forecasting these dynamically important flow features.