Activities carried out over the last three decades in relation to core-concrete interactions and melt coolability, as well as related containment failure modes, have significantly increased the level of understanding in this area. In a severe accident with little or no cooling of the reactor core, the residual decay heat in the fuel can cause the core materials to melt. One of the challenges in such cases is to determine the consequences of molten core materials causing a failure of the reactor pressure vessel. Molten corium will interact, for example, with structural concrete below the vessel. The reaction between corium and concrete, commonly referred to as MCCI (molten core concrete interaction), can be extensive and can release combustible gases. The cooling behaviour of ex-vessel melts through sprays or flooding is also complex. This report summarises the current state of the art on MCCI and melt coolability, and thus should be useful to specialists seeking to predict the consequences of severe accidents, to model developers for severe-accident computer codes and to designers of mitigation measures.