The state of the art in modeling reflooding situations, mainly with the two-fluid system analysis codes, is reviewed; certain related general code development issues are included. Our current modeling of reflooding is reasonable and can be made sufficiently conservative for safety assessments, but it is not outstanding. Fundamental understanding of the detailed two-phase flow and heat transfer mechanisms has not progressed significantly over the state already available several years ago. The better understanding of system behavior achieved by the coordinated program of large-scale experiments is summarized and its impact on the modeling work discussed. In the future, factors such as the additional accident scenaria now considered, the new and advanced reactor types being analyzed, and the geometric growth of computing capacity are likely to drive our efforts. The new requirements and challenges can be met best by building into the codes pieces of understanding of the actual physical processes at the most fundamental level practicable. The discussion focuses on the existing codes and their successes and shortcomings; both certain specialized and the more complex general-purpose system codes are considered. The aim is not to conduct an exhaustive review of all aspects of the problem, but rather to reach consensus on certain issues.