The cut cone C_n is the cone generated by the cuts of the complete graph on n nodes. In this paper, we present a survey of the known results on the facial structure of the cut cone C_n and of the related cut polytopeAvailable from TIB Hannover: RN 4052(91722) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman