Density-limit discharges in the W7-AS stellarator, with constant line-integrated density and a duration of up to 2 s, were studied at three values of the toroidal magnetic field (B = 0.8, 1.25 and 2.5 T). The central factor governing the physics of the density limit in stellarators was demonstrated to be the decreasing net power to the plasma when the centrally peaked radiated power density profile exceeds that of the deposited power density. The process was further accelerated by the peaking of electron density under these conditions. In discharges with B = 2.5 T, simulations of the centrally peaked radiation power density profiles could be shown to be due to peaked impurity density profiles. Laser blow off measurements clearly inferred an inward pinch of the injected aluminium. These discharges had the electron density profile form found in the improved confinement H-NBI mode on W7-AS.The aim of producing steady-state discharges at the highest possible density in stellarators is naturally of special interest for reactor operation. Such a scenario has been best achieved in H-mode discharges, in which ELMs restricted the impurity influx to the plasma and an equilibrium in the plasma parameters with suitably low radiation power levels was possible. A density scan in ECRH discharges highlights the need to control impurity sources and choose electron densities well below the density limit in order that steady-state operation can be attempted in discharges without ELMs.A simple model of bulk radiation predicted that the limiting densityshould depend on the square root of heating power and this wasexperimentally confirmed. The magnetic field scaling of the limitingdensity found experimentally in this simple model will partly dependon the term concerning the radial profile of the impurity density,which in turn is a function of the diffusion coefficient and inwardpinch of the impurity ions. Theoretical studies have shown that anassumption about the B dependence of the thermal conductivity leadsto density limit scaling laws with an explicit B dependence.