The recent progression in electronics and humankind's increased dependence on electronic gadgets have significantly impacted energy supply and demand metrics. In the past, batteries have been able to meet these demands adequately. However, their low power density (Ps) has inspired alternative energy storage advancements that can foster a transition to net‐carbon‐zero via renewables. Supercapacitor (SC) innovations, such as the recent emergence of solid‐state supercapacitors (SSCs), have gained tremendous attention owing to their mechanical robustness, safety, possible flexibility, long cycle life, portability, prospective high Ps, and suitability for advanced energy technologies. Complimentary to the affordable and lightweight material design requirements is the enormous potential of the graphene family in SSCs owing to facile synthesis advantages, easy scalability and, processing high electrical conductivity, low costs, and mechanical robustness among others. Therefore, the review highlights the recent efforts to advance SSCs with the graphene family in electrodes and electrolytes. The work discusses SC basic concepts and main characterization techniques, and applications of the graphene family in both electrolytes and electrodes of SSCs. Finally, the merits, demerits and prospects of incorporating graphene derivatives to advance SSC performance and sustainability are outlined. Key research directions, including machine learning, are also recommended from the reviewed studies.