The ITER scenarios and the project of DEMO involve stable operation above the Greenwald density, which justifies efforts to understand and overcome the density limit, observed as a disruptive termina-tion of tokamak discharges and a thermal crash (with no disruption) of stellarator and reversed-field pinch (RFP) ones. Both in the tokamak and the RFP, new finds show that the high density limit is not governed by a unique, theoretically well-determined physical phenomenon, but by a com-bination of complicated mechanisms involving two-fluid effects, electrostatic plasma response to magnetic islands and plasma-wall interaction. In this paper we will show new evidence challenging the traditional picture of the " Greenwald limit " , in particular with reference to the role of thermal instabilities and the edge radial electric field E r in the development of this limit.