In achieving "carbon neutrality," the new power system faces a range of security challenges. These include the emergence of coupled faults in AC and DC systems, as well as an increased risk to frequency and voltage stability. Consequently, there is a growing interest in integrating energy storage technology into security control measures. To better understand the role of energy storage in enhancing system security, it is essential to outline the relevant scenarios, theories, and technical approaches. This will provide critical support to the power system while identifying key areas of future research. This paper focuses on five key aspects: static and dynamic security of the power system, security considerations in AC/DC hybrid power systems, active security technologies, and the ancillary service market. These areas encompass the progress made in understanding the relationship between energy storage and grid reliability, frequency stability, voltage stability, transmission blockage, and DC blocking cascading trip prevention. The research highlights the significance of examining the state of charge (SOC) reserve capabilities of energy storage, investigating the multi-timescale coupling between energy storage and other regulating resources, and improving the market mechanisms to facilitate energy storage's participation in emergency security regulation services. These findings provide valuable insights for advancing the research on energy storage's role in enhancing security in the evolving power systems.