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• Different methods and possible solutions in cyber security in SGs are summarized. • The interactive features of cyber security, modeling and mechanisms are discussed in detail. • The characteristics and applicability of various cyber-attack models are technically presented and analyzed. • The cutting-edge cyber security techniques in SGs and energy systems in various research are discussed. • Possible potential research directions regarding CPSs are highlighted. • Decisive problem-solving approaches are analyzed and concluded comprehensively. Due to the advancement in communication networks, metering and smart control systems, as well as the prevalent use of Internet-based structures, new forms of power systems have seen moderate changes with respect to several aspects of contradictory Cyber–Physical Power Systems (CPPSs). These structures usually have connections between power sections and cyber parts. CPPSs confront newly emerging issues including stability, resiliency, reliability, vulnerability and also security. Studying, analyzing and providing solutions to mitigate or solve these problems highly depend on accurate modeling methods and examining the interaction mechanisms associated with the cyber-security of Smart Grids (SGs). This paper aims to systematically summarize different methods and techniques and to review corresponding solution approaches in cyber-security in energy systems. In the first step, we discuss the interactive features of cyber-security; then, their modeling and mechanisms are reviewed and summarized in detail. Furthermore, the characteristics and applicability of different cyber-attack models are technically discussed and analyzed. The cutting-edge cyber security approaches such as blockchain and quantum computing in SGs and power systems are stated, and recent research directions are highlighted. The decisive problem-solving approaches and defense mechanisms are presented. Finally, some points regarding the role of cyber-security in the future of SGs are presented. [ABSTRACT FROM AUTHOR]