Organic material electrodes are regarded as promising candidates for next-generation rechargeable batteries due to their environmentally friendliness, low price, structure diversity, and flexible molecular structure design. However, limited reversible capacity, high solubility in the liquid organic electrolyte, low intrinsic ionic/electronic conductivity, and low output voltage are the main problems they face. A lot of research work has been carried out to explore comprehensive solutions to the above problems through molecular structure design, the introduction of specific functional groups and specific molecular frameworks, from small molecules to polymer molecules, metal-organic frameworks (MOFs), covalent organic frameworks (COFs) and heterocyclic molecules; from simple organic materials to organic composites; from single functional groups to multi-functional groups; etc. The inevitable relationship between various molecular structure design and enhanced electrochemical properties has been illustrated in detail. This work also specifically discusses several approaches for the current application of organic compounds in batteries, including interfacial protective layer of inorganic metal oxide cathode, anode (metal lithium or silicon) and solid-state electrolyte, and host materials of sulfur cathode and redox media in lithium-sulfur batteries. This overview provides insight into a deep understanding of the molecular structure of organic electrode materials (OEMs) and electrochemical properties, broadens people’s research ideas, and inspires researchers to explore the advanced application of electroactive organic compounds in rechargeable batteries.