Multifunctional electrodes for structural supercapacitors are prepared by vacuum infiltration of single-walled carbon nanotubes (SWCNTs) into woven carbon fibers (CFs); the use of reductive charging chemistry to form nanotubide solutions ensured a high degree of individualization. The route is highly versatile, as shown by comparing four different commercial nanotube feedstocks. In film form, the pure nanotubide networks (“buckypapers”) are highly conductive (up to 2000 S cm−1) with high surface area (>1000 m2 g−1) and great electrochemical performance (capacitance of 101 F g−1, energy density of 27.5 Wh kg−1 and power density of 135 kW kg−1). Uniformly integrating these SWCNT networks throughout the CF fabrics significantly increased electrical conductivity (up to 318 S cm−1), surface area (up to 196 m2 g−1), and in-plane shear properties, all simultaneously. The CNT-infiltrated CFs electrodes exhibited intrinsically high specific energy (2.6–4.2 Wh kg−1) and power (6.0–8.7 kW kg−1) densities in pure 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM TFSI) electrolyte. Multifunctional structural supercapacitors based on CNT-coated CFs offer a substantial increase in capacitive performance while maintaining the tensile mechanical properties of the as-received CF-based composite. This non-damaging approach to modify CFs with highly graphitic, high surface area nanocarbons provides a new route to structural energy storage systems.