The growing renewable energy consumption has stimulated the rapid development of diverse energy storage systems (ESSs) in our electronic society. As a successful representative, lithium-ion batteries (LIBs) play a vital role in meeting today's energy storage demand. However, LIBs are plagued by intrinsic unsafety and detrimental environmental contamination. In this respect, rechargeable aqueous zinc-ion batteries (ZIBs) and supercapacitors (SCs) as potential alternatives have attracted considerable attention due to their characteristics such as innate safety, environmental friendliness, cost-effectiveness, competitive gravimetric energy density, and loose fabrication process. Inspired by these merits, massive efforts have been devoted to designing and exploring high-performance aqueous Zn-based energy storage devices. The key for advanced Zn-based energy storage devices is to exploit high-performance cathode materials. Covalent organic frameworks (COFs) are an emerging class of organic polymer with periodic skeletons showing attractive properties in structural tunability, well-defined porosity, functional versatility, and high chemical stability. The distinguishing features of COFs make them promising electrode materials for electrochemical energy storage applications. However, the electrochemical storage capability and charge storage mechanism of COF materials have been rarely investigated, and their potential applications have not been evaluated yet so far. In this thesis, COFs are proposed as cathode materials for rechargeable aqueous Zn-ion energy storage. Initially, a new phenanthroline COF (PA-COF) material was synthesized and used as an electrode for Zn-ion supercapatteries (ZISs) for the first time. The as-synthesized PA-COF shows abundant nucleophilic sites and suitable pore structure, demonstrating the efficient storage capability of Zn2+ and H+. Further, hexaazatriphenylene-based COF (HA-COF) material with and without precisely grafted quinone functional groups has been proposed to understand structure-activity relationships. In this chapter, the influence of quinone groups on the electrochemical performance of HA-COF has been systematically studied, disclosing an enhancement coordination capability of Zn ions against protons in the quinone-functionalized HA-COF. Lastly, we synthesized a radical benzobisthiazole COF (BBT-COF) and deeply investigated the electrochemical performance. As expected, this COF electrode shows an ultrastable cycling performance and demonstrates a radical reaction pathway.