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, this last observed as a disruptive termination 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 findings show that the high density limit is not governed by a unique, theoretically well-determined physical phenomenon, but by a combination of complex 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 Er in the development of this limit. © 2015 EURATOM.