Due to their outstanding electrochemical properties, electrical conductivity, flexibility, and low-cost, carbon materials open up new opportunities for the design of compact devices with a wide variety of potential applications. Biomass renewable resources for carbon material preparation have attracted huge attention in the last few years due to their widespread availability, low-cost processability and high-performance of the resulting porous carbons for sustainable technological applications. For example, the porosity and morphology of carbon materials, which can be tuned by different activation methods, govern the ion diffusion rate during supercapacitor charge/discharge processes. On the other hand, carbon electrodes have been applied as electrodes for dye-sensitized and perovskite solar cells, thanks to their low fabrication cost, compact structure, and optimized interfaces, which play a key role in the charge collection and stability of the devices. Moreover, due to the possibility of using carbon electrodes for storage and conversion devices, efficient methods to harvest and store energy in one single device are crucial for technological advancement and the energy transition process. This contribution aims to review the advances made in the use of carbon materials obtained from biomass sources as electrodes for storage and energy conversion devices, and the future application of shared and/or distinct carbon electrodes for the development of integrated power packs including supercapacitors and dye-sensitized or perovskite solar cells. The storage properties of supercapacitors are discussed in terms of the textural characteristics of biomass-derived activated carbons while the photovoltaic parameters of solar cells based on bio-sourced carbons are compared with those of devices using conventional metal-based electrodes. Finally, special emphasis is placed on the energy conversion–storage efficiencies of solar cell-supercapacitor integrated devices.