The aim of this editorial article is to provide some structuring of the subject addressed in this part of the issue, which, in the view of the present authors, has not that clearly been reached by the specific contributions. Ex-vessel corium behavior is a wide field. Therefore, classification of the goals of investigations within a safety philosophy is especially required to get not lost in detailed aspects. The overall goals here are the coolability and retention options under ex-vessel conditions. Based on scenario considerations generally addressing risks and options, general principles of cooling and retention devices are outlined. Since the concrete erosion by melt yields a major risk and has to be considered in the concepts and devices, and also since several contributions to this part are dealing with specific aspects of this molten core-concrete interaction (MCCI), a large part of this editorial paper concerns the status of knowledge and modeling and the lines of research in this area. The status and the perspectives of codes is especially addressed by own contributions of one of the authors with the GRS code WEX and with MEDICIS, both codes included in the European integral code ASTEC. Finally, the coolability questions are discussed with respect to the different concepts in general and those addressed specifically in the present contributions. In some considerations, gas production by erosion plays a role to produce porous or particulate debris and thus to enhance coolability. Water injection from bottom is a more direct and probably more effective measure to reach this, specifically designed in the COMET core catcher concept. Specific contributions in this part deal with this concept, which is most closely related to the general subject of the present issue. (c) 2006 Elsevier B.V. All rights reserved.