Abstract The behavior of LMFBR core debris following a hypothetical core-disruptive accident (HCDA) depends upon a wide range of physical and chemical phenomena. Current understanding of the key phenomena are summarized for core-debris behavior within the reactor vessel, within the reactor cavity, and within the concrete base mat below the reactor cavity. In-vessel behavior was the principal consideration of post-accident heat removal for the FFTF reactor. Several concepts of engineered core-retention systems within the reactor cavity have been considered for other reactors, including the cooled crucible concept, the sacrificial barrier concept, the stable barrier concept, and the catch tray concept. Behavior within the concrete base mat is an important part of a general concept of inherent core retention which depends upon an understanding of the complex interactions of core debris with concrete.