Battery electric vehicles (BEVs) are the most interesting option available for reducing CO2 emissions for individual mobility. To achieve better acceptance, BEVs require a high cruising range and good acceleration and recuperation. To meet these requirements, hybrid energy storage systems can be used, which combine high-power (HP) and high-energy (HE) storage units. To date, the coupling of the two energy storage types has been realized passively or actively by using DC/DC converters. In this paper, the corresponding topologies, described in the literature, are presented and reviewed with focus on the usable voltage window of the energy storage types, the utilization of stored energy, the connection to a power train/load, and additionally required power electronics. Besides, reconfigurable topologies on cell level and module level, without the need of additional DC/DC converters, have been investigated in the literature and are also presented and reviewed. We then suggest a new topology class of discrete hybrid energy storage topologies, which combine both research topics. In the proposed topology class, standardized energy storage modules (ESMs) consisting of either HP or HE devices are combined. Each ESM is equipped with switching elements, which can activate, bypass, or disable the module and therefore allow reconfigurations. Four sub-topologies emerge when these ESMs are arranged to form an energy storage system.