Abstract: Under the "dual-carbon" framework, it is an inevitable trend for conventional power systems to evolve into new power systems characterized by a primary reliance on renewable energy sources (RES). A high penetration of RES, integrated into the grid via power electronic devices, significantly diminishes the system's inertial support capability, thereby exacerbating frequency security issues. Inertia is crucial for ensuring frequency security. This paper provides a comprehensive review of the research achievements and progress in the estimation, requirements, and optimization of system inertia in power systems worldwide. Additionally, it offers discussions on potential future directions and prospects. Initially, the concept and components of system equivalent inertia are explained from an energy viewpoint. Secondly, to accurately estimate the equivalent inertia support capabilities of individual devices and the overall system, the current inertia estimation methods are categorized and described based on the type of power synchronization and disturbance. Based on the inertia estimation, this paper summarizes the research pathways and current status of low-inertia power systems from two perspectives: system inertia requirements based on frequency deviation and rate of change of frequency, and inertia-optimized operation based on unit commitment and spatial distribution characteristics. In conclusion, drawing from current research outcomes, this study provides an overview of the future research directions related to inertia in the new type power systems.