Hydrogen production and combustion during hypothetical severe nuclear reactor accidents are discussed from the perspective of integral predictive assessment of such accidents. Unmitigated hydrogen production after prolonged core dryout has the adverse impacts of accelerating the degradation of core geometry, reducing heat transfer area, and impeding the in-vessel recovery of an accident. Unmitigated hydrogen combustion can, in certain circumstances, lead to containment failure, or it could damage equipment and thereby impede recovery. The phenomena of in-vessel hydrogen generation and combustion are summarized, including recent experiments, and selected models for integral predictive assessment of these phenomena are described. Adequacies and shortcomings of models and the experimental data base are identified, and the effects of mitigation are discussed.