The advantages provided by multiwalled carbon nanotubes (CNTs) as backbones for composite supercapacitor electrodes are discussed. This paper particularly highlights the electrochemical properties of carbon composites obtained by pyrolysis of seaweed/CNTs blends. Due to the nanotexturing effect of CNTs, supercapacitors fabricated with electrodes from these composites exhibit enhanced electrochemical performances compared with CNT-free carbons. The cell resistance is dramatically reduced by the excellent conductivity of CNTs and by the good propagation of ions favored by the presence of opened mesopores. As a consequence, the specific power of supercapacitors based on these nanocomposites is very high. Another advantage related to the presence of CNTs is a better life cycle of the systems. The composite electrodes are resilient during the charge/discharge of capacitors; these are able to perfectly accommodate the dimensional changes appearing in the active material without mechanical damages.