Structural supercapacitors (SSCs) are multifunctional energy storage composites (MESCs) that combine the mechanical properties of fiber-reinforced polymers and the electrochemical performance of supercapacitors to reduce the overall mass in lightweight applications with electrical energy consumption. These novel MESCs have huge potentials, and their properties have improved dramatically since their introduction in the early 2000’s. However, the current properties of SSCs are not sufficient for complete energy supply of electrically driven devices. To overcome this drawback, the aim of the current study is to identify key areas for enhancement of the multifunctional performance of SSCs. Critical modification paths for the SSC constituents are systematically analyzed. Special focus is given to the improvement of carbon fiber-based electrodes, the selection of structural electrolytes and the implementation of separators for the development of more efficient SSCs. Finally, current SSCs are compared in terms of their multifunctionality including material combinations and modifications.