The impermeability theorem (IT) states that there is no flux of Ertel's potential vorticity (PV) across an isentropic surface. These fluxes are key contributors to PV budgets of air volumes. It is shown by retracing the derivation of this theorem and by analyzing the flux terms that the IT relies on a specific choice of the fluxes. There are several other physically equivalent formulations where fluxes of PV across an isentropic surface occur. The reasons for these discrepancies are explained as are the consequences for our understanding of the general circulation of the atmosphere. Quasigeostrophic PV fluxes and their relation to the Eliassen-Palm flux are briefly discussed. Reanalysis data are used to evaluate some PV-fluxes in a climatological context.