As the world’s demand for sustainable and reliable energy source intensifies, the need for efficient energy storage systems has become increasingly critical to ensuring a reliable energy supply, especially given the intermittent nature of renewable sources. There exist several energy storage methods, and this paper reviews and addresses their growing requirements. In this paper, the energy storage options are subdivided according to their primary discipline, including electrical, mechanical, thermal, and chemical. Different possible options for energy storage under each discipline have been assessed and analyzed, and based on these options, a handsome discussion has been made analyzing these technologies in the hybrid mode for efficient and reliable operation, their advantages, and their limitations. Moreover, combinations of each storage element, hybrid energy storage systems (HESSs), are systems that combine the characteristics of different storage elements for fulfilling the gap between energy supply and demand. HESSs for different storage systems such as pumped hydro storage (PHS), battery bank (BB), compressed air energy storage (CAES), flywheel energy storage system (FESS), supercapacitor, superconducting magnetic coil, and hydrogen storage are reviewed to view the possibilities for hybrid storage that may help to make more stable energy systems in the future. This review of combinations of different storage elements is made based on the previous literature. Moreover, it is assessed that sodium-sulfur batteries, lithium-ion batteries, and advanced batteries are the most helpful element in HESSs, as they can be hybridized with different storage elements to fulfill electricity needs. The results also show that HESSs outperformed other storage systems and, hence, hybridizing the characteristics of different storage elements can be employed for optimizing the performance of energy storage systems.