The containment of a nuclear reactor is a component whose loss in an accident has serious consequences on property, persons, and environment. The Fukushima accident reminded us of this reality. For more than 30 years, the French Nuclear Energy and Alternative Energies Commission has been conducting research on the failure modes of these enclosures, particularly on their slow pressurization during a steam release and hydrogen risk. Significant progress has been made on wall condensation and its spatial distribution, the occurrence and erosion of gas stratification, and the impact of mitigation systems, such as spraying and catalytic recombiners. This knowledge has been included in numerical tools and internationally recognized expertise. These tools have also been used for the safety of the hydrogen energy industry. The emergence of new systems, particularly passive systems and new light water reactor concepts, has led us to examine new questions that will have to be addressed in the coming years. This examination is done in view of current computational fluid dynamics code capabilities and limitations.