As the share of variable renewable energy sources in power systems grows, system operators have encountered several challenges, such as renewable generation curtailment, load interruption, voltage regulation problems, and frequency stability threats. This is particularly important for power systems transitioning to net zero. Energy storage systems are considered an effective solution to overcome these challenges. However, with the increasing penetration of renewable energy sources, different requirements have emerged, and a single energy storage solution may not effectively meet all of them. Hybrid energy storage systems have recently been proposed to remedy this problem. Different individual energy storage systems possess complementary characteristics that can enhance the reliability, security, and stability of power systems. However, hybrid energy storage systems often require more intricate modeling approaches and control strategies. Many researchers are currently working on hybrid energy storage systems to address these issues. This paper thoroughly reviews the modeling and control schemes of hybrid energy storage systems for different power system operation studies. It also examines the factors influencing the selection of hybrid energy storage systems for various power system applications. Finally, this paper provides recommendations for future research in this area.