Density limit investigations on ASDEX have been performed under a variety of conditions: ohmically heated and neutral injection heated plasmas in H2, D2 and He have been studied in different divertor configurations, after various wall coating procedures, with gas puff and pellet fuelling, and in different confinement regimes with their characteristically different density profiles. A detailed description of the parametric dependence of the density limit, which in all cases is a disruptive limit, is given. This limit is shown to be a limit to the density at the plasma edge. Therefore, the highest densities corresponding to neRqa/Bt>30*1019 m-2.T-1 are obtained with centrally peaked ne profiles. Radiation from the main plasma at the density limit is always significantly below the total input power. The plasma disruption is due to an m=2 instability which for medium and high qa is preceded by one or more minor disruptions. In this range of qa, the disruptive instability is initiated by the occurrence of a Marfe on the high field side as a consequence of strong plasma cooling in this region. The duration of the Marfe increases with increasing distance between the plasma edge and the q=2 surface. After penetrating onto closed flux surfaces the Marfe leads to a current contraction and a subsequent destabilization of the m = 2 mode. In helium plasmas a strongly radiating, poloidally symmetric shell is observed before the density limit instead of a Marfe. An instantaneous destabilization of this mode is observed at low qa. Detailed measurements of plasma edge and divertor parameters close to the density limit indicate the development of a cold, dense divertor plasma before the disruption. Models describing the scrape-off layer and the divertor region predict an upper limit to the edge density at low divertor temperatures according to power balance considerations. Their relations to the experimental findings, especially the low field side cooling, ar