Cyber-Physical System (CPS) is a new kind of digital technology that increases its attention across academia, government, and industry sectors and covers a wide range of applications like agriculture, energy, medical, transportation, etc. The traditional power systems with physical equipment as a core element are more integrated with information and communication technology, which evolves into the Cyber-Physical Power System (CPPS). The CPPS consists of a physical system tightly integrated with cyber systems (control, computing, and communication functions) and allows the two-way flows of electricity and information for enabling smart grid technologies. Even though the digital technologies monitoring and controlling the electric power grid more efficiently and reliably, the power grid is vulnerable to cybersecurity risk and involves the complex interdependency between cyber and physical systems. Analyzing and resolving the problems in CPPS needs the modelling methods and systematic investigation of a complex interaction between cyber and physical systems. The conventional way of modelling, simulation, and analysis involves the separation of physical domain and cyber domain, which is not suitable for the modern CPPS. Therefore, an integrated framework needed to analyze the practical scenario of the unification of physical and cyber systems. A comprehensive review of different modelling, simulation, and analysis methods and different types of cyber-attacks, cybersecurity measures for modern CPPS is explored in this paper. A review of different types of cyber-attack detection and mitigation control schemes for the practical power system is presented in this paper. The status of the research in CPPS around the world and a new path for recommendations and research directions for the researchers working in the CPPS are finally presented.