Currently, the electrification of transport networks is one of the initiatives being performed to reduce greenhouse gas emissions. Despite the rapid advancement of power electronic systems for electrified transportation systems, their integration into the AC power grid generates a variety of quality issues in the electrical distribution system. Among the possible solutions to this challenge is the inclusion of continuous storage systems, which can be located either onboard or offboard. The rapid development of energy storage devices has enabled the creation of numerous solutions that are leading to ever-increasing energy consumption efficiency, particularly when two or more of these storage systems are linked in a cascade and a hybrid mode. The various energy storage systems that can be integrated into vehicle charging systems (cars, buses, and trains) are investigated in this study, as are their electrical models and the various hybrid storage systems that are available.