Organic electrode materials (OEMs) can deliver remarkable battery performance for metal-ion batteries (MIBs) due to their unique molecular versatility, high flexibility, versatile structures, sustainable organic resources, and low environmental costs. Therefore, OEMs are promising, green alternatives to the traditional inorganic electrode materials used in state-of-the-art lithium-ion batteries. Before OEMs can be widely applied, some inherent issues, such as their low intrinsic electronic conductivity, significant solubility in electrolytes, and large volume change, must be addressed. In this review, the potential roles, energy storage mechanisms, existing challenges, and possible solutions to address these challenges by using molecular and morphological engineering are thoroughly summarized and discussed. Molecular engineering, such as grafting electron-withdrawing or electron-donating functional groups, increasing various redox-active sites, extending conductive networks, and increasing the degree of polymerization, can enhance the electrochemical performance, including its specific capacity (such as the voltage output and the charge transfer number), rate capability, and cycling stability. Morphological engineering facilitates the preparation of different dimensional OEMs (including 0D, 1D, 2D, and 3D OEMs) via bottom-up and top-down methods to enhance their electron/ion diffusion kinetics and stabilize their electrode structure. In summary, molecular and morphological engineering can offer practical paths for developing advanced OEMs that can be applied in next-generation rechargeable MIBs.