The year 2016 marks the 30th anniversary of the accident in the No. 4 unit of the Chernobyl NPP and the 5th anniversary of the accident at the Fukushima NPP in Japan. The Chernobyl accident substantially changed the public's attitude toward severe accidents at NPPs, promoting on the one hand modernization and improvement of safety systems and on the other hand a higher safety culture by harmonization of standards and regulations, and adoption of deeply echeloned protection and a scientifically validated approach to the analysis of accidents. The Fukushima accident revealed a new class of accidents - extreme actions caused by naturally occurring cataclysms and/or different external actions, which actually are identical to loss of a large part or all of the means for controlling an accident. The present article examines the main lessons on accidents in terms of understanding the phenomenology of the events occurring during severe accidents and confirms the importance of the deterministic component of the safety concept. At the same time, it emphasizes that special attention must be given to hydrogen safety, systems for prolonged removal of residual heat, emergency readiness, and emergency response under the extreme conditions of severe accidents. The computational means used to develop accident counter-measures must be properly set to take account of the design features of the reactor facility, the containment of the NPP, and the adjoining territories in order to determine the time required to implement the procedures for controlling accidents and mitigating the consequences.