Seismic safety of nuclear power plants became an eminent importance after the Great Tohoku earthquake on 11th of March, 2011 and subsequent disaster of the Fukushima Dai-ichi nuclear power plant. Intensive works are in progress all over the world that include review of the site seismic hazard assessment, revision of the design bases, evaluation of vulnerability, and development of accident management capabilities of the plants. The lessons learned from the Fukushima-accident changed the paradigm of the design. Preparedness to the impossible, id est the development of means and procedures for ensuring the plant safety in extreme improbable situations became great importance. Main objective of the Chapter is to provide brief insight into the actual issues of seismic safety of nuclear power plants, provide interpretation of these issues, and show the possible solutions and scientific challenges. The "specific-to-nuclear" aspects of the characterisation of seismic hazard, including fault displacement are discussed. The actual design requirements, safety analysis procedures are briefly presented with main focus on the design extension situations. Operation aspects and problems for restart after earthquake are also discussed. The Chapter is more focusing on seismic safety of the inland plants, located on soil sites, in low-to-moderate (diffuse) seismicity regions.