The operation of the electricity network has grown more complex due to the increased adoption of renewable energy resources, such as wind and solar power. Using energy storage technology can improve the stability and quality of the power grid. One such technology is flywheel energy storage systems (FESSs). Compared with other energy storage systems, FESSs offer numerous advantages, including a long lifespan, exceptional efficiency, high power density, and minimal environmental impact. This article comprehensively reviews the key components of FESSs, including flywheel rotors, motor types, bearing support technologies, and power electronic converter technologies. It also presents the diverse applications of FESSs in different scenarios. The progress of state-of-the-art research is discussed, emphasizing the use of artificial intelligence methods such as machine learning, digital twins, and data-driven techniques for system simulation, fault prediction, and life-assessment research. The article also addresses the challenges related to current research and the application of FESSs. It concludes by summarizing future directions and trends in FESS research, offering valuable information for further advancement and improvement in this field.