The research network "Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models" was organized with European funding (COST Action E50905) for the period of 2010-2014. Its extensive brainstorming suggests how the subgrid-scale parameterization problem in atmospheric modeling, especially for convection, can be examined and developed from the point of view of a robust theoretical basis. Our main cautions are current emphasis on massive observational data analyses and process studies. The closure and the entrainment detrainment problems are identified as the two highest priorities for convection parameterization under the mass flux formulation. The need for a drastic change of the current European research culture as concerns policies and funding in order not to further deplete the visions of the European researchers focusing on those basic issues is emphasized.