A severe accident (SA) is defined as an incident involving melting of the nuclear reactor core and the release of fission products (FP) from the fuel and their associated risks. In the SA, the containment may fail, causing the public hazard of fission products released to the environment. This review elaborates the resolved issues of SAs under the condition of a hypothetical SA. SA research that has been performed over the years is briefly described, including various SA scenarios. The SA scenarios involve core melt scenarios from the beginning of core degradation to melt formation and relocation into the lower head and to the containment, the interactions of the molten corium with water and concrete, the behavior of fission products in- and ex-vessel, hydrogen-related phenomena, and all associated risks. The mitigation strategies that have been adopted in existing reactors and advanced light water reactors (ALWR) are also discussed. These mitigation measures can keep the reactor vessel or containment intact and terminate the SA progression. SA analysis codes are then summarized and divided into three categories, namely, systematic analysis codes, mechanism analysis codes, and single-function analysis codes. Next, the unresolved issues of SAs are proposed, including narrow gap cooling, melt chemical interactions, steam explosion loads, molten debris coolability, and iodine chemistry. Further experimental and theoretical research activities should be conducted to resolve these issues; consequently, some recommendations for further research work are also given in the last part of this review. This review aims to add to the knowledge and understanding of SA research in the past few decades and to benefit further research of SAs.