The analyses performed to evaluate the capacity to contain the core materials after a hypothetical core meltdown accident are generally grouped under the area of post-accident heat removal (PAHR). Substantial advancement in the state-of-the-art of the PAHR area has occurred within the last few years. The key issues of PAHR, as applied to safety analyses of liquid-metal breeder reactors, are summarized in this Review. The Review includes heat source strength for post-accident conditions, in-vessel core debris retention, ex-vessel core debris retention, and the effects of alternative fuel materials.