Over recent decades, a new type of electric energy storage system has emerged with the principle that the electric charge can be stored not only at the interface between the electrode and the electrolyte but also in the bulk electrolyte by redox activities of the electrolyte itself. Those redox electrolytes are promising for non-flow hybrid energy storage systems, or redox electrolyte-aided hybrid energy storage (REHES) systems; particularly, when they are combined with highly porous carbon electrodes. In this review paper, critical design considerations for the REHES systems are discussed as well as the effective electrochemical characterization techniques. Appropriate evaluation of the electrochemical performance is discussed thoroughly, including advanced analytical techniques for the determination of the electrochemical stability of the redox electrolytes and self-discharge rate. Additionally, critical summary tables for the recent progress on REHES systems are provided. Furthermore, the unique synergistic combination of porous carbon materials and redox electrolytes is introduced in terms of the diffusion, adsorption, and electrochemical kinetics modulating energy storage in REHES systems.