All-polymer and paper-based energy storage devices have significant inherent advantages in comparison with many currently employed batteries and supercapacitors regarding environmental friendliness, flexibility, cost and versatility. The research within this field is currently undergoing an exciting development as new polymers, composites and paper-based devices are being developed. In this report, we review recent progress concerning the development of flexible energy storage devices based on electronically conducting polymers and cellulose containing composites with particular emphasis on paper-based batteries and supercapacitors. We discuss recent progress in the development of the most commonly used electronically conducting polymers used in flexible device prototypes, the advantages and disadvantages of this type of energy storage devices, as well as the two main approaches used in the manufacturing of paper-based charge storage devices.