The rising trend of green energy has made it necessary to utilise efficient green materials in electrochemical energy storage devices (EESDs) under a green economy. The need for sustainable energy storage technologies due to the rising demand for energy, improved technology, and the huge challenge of E-waste requires the development of eco-friendly advanced materials and recycling processes in electrochemical energy storage within a circular economy framework. This paper focuses on cellulose, shellac, polylactic acid (PLA), chitin, and chitosan due to their exceptional sustainability, biodegradability, and functional properties and explore how these polymers can improve the circular economy for batteries and supercapacitors by following the aspects of their background, processing and preparation methods, properties, chemical structures, applications, and recent development. As such, this review promotes the increased utilisation of biodegradable biopolymers within the circular economy of EESDs, particularly for future technologies such as flexible, wearable, stretchable, and transparent devices. This review raises awareness of these materials' capability to improve sustainability and recyclability, thus promoting increased use and integration of these materials into EESDs leading to green technologies and low environmental impact.