With the advancement of data-acquisition systems, information technology, and network technologies, the energy and power system has entered the deep integration of the cyber and physical sides as known as cyber-physical energy and power system (CPEPS) leading to more attention from researchers and practitioners in industry. The feedback loops in which physical processes affect cyber parts and vice versa, therefore, can gain greater efficiency, resilience, and intelligence through the data exchange process between two layers. The concept of CPEPS has been existed for a long time and its applications are gradually increasing in the real world, however, there has been still many potential risks and challenges in the research and development process. Simulation method is a common and simple approach for the purpose of analyzing, evaluating, and considering solutions before actual implementation. For this purpose, this paper provides first the framework of CPEPS, and current applications and challenges that researchers are facing. Then, the next section is the overview of simulation methods with different software and tools in CPEPS research in order to provide researchers with an optimal approach to the ongoing and further research towards the transition of digitalization on energy and power system.