Considering the in-vessel-retention strategy for the management of severe accident in light water reactors, this paper provides an overview of state-of-the-art modelling under transient conditions of the core melt behaviour in the lower head. This presentation is based on a cross-comparison between the models of four different codes, namely, ASTEC (IRSN), HEFEST (IBRAE), EDF proprietary version of MAAP5 (EPRI) and PROCOR (CEA) and is illustrated by some results from a recent benchmark exercise carried out in the frame of the European IVMR project. Apart from pool thermal-hydraulics and vessel wall ablation, some emphasis is put on melt thermochemistry and transient phase segregation (boundary crust formation/disappearance and liquid phase stratification). As highlighted in the benchmark exercise, the main associated uncertainties in terms of heat flux at the vessel wall external boundary are related to the stratification transients and the stability of the crusts in contact with light metal layer during stratification inversion transient.