Major European weather forecast centers are moving aggressively toward the horizontal mesh size of 1–5 kilometers with their regional models. Such a high horizontal resolution (convection-permitting limit) marginally resolves moist deep convection. To discuss new challenges for convection parameterization under such a limit, the European Cooperation in the Field of Scientific and Technical Research (COST) Action ES0905 organized a workshop in which 33 scientists from 14 European countries met at the Polish Academy of Sciences. The participants found that in the convection-permitting limit, only one convective tower (a basic element of deep moist cumulus convection) would exist within a given grid box. A traditional notion of equilibrium within a standard framework no longer works. Evolution of a parameterized convective tower can be described only if it is directly coupled with the resolved flows.