Corium behavior in the lower plenum of the reactor vessel during a severe accident is very important, as this affects a failure mechanism of the lower head vessel and a thermal load to the outer reactor vessel under the IVR-ERVC (In-Vessel corium Retention through External Reactor Vessel Cooling) condition. This paper discusses the state of the art and technical issues on corium behavior in the lower plenum, such as initial corium pool formation characteristics and its transient behavior, natural convection heat transfer in various geometries, natural convection heat transfer with a phase change of melting and solidification, and corium interaction with a lower head vessel including penetrations of the ICI (In-Core Instrumentation) nozzle are discussed. It is recommended that more detailed analysis and experiments are necessary to solve the uncertainties of corium behavior in the lower plenum of the reactor vessel.