Composites of carbon nanotubes and conducting polymers can be prepared via chemical synthesis, electrochemical deposition on preformed carbon nanotube electrodes, or by electrochemical co-deposition. The composites combine the large pseudocapacitance of the conducting polymers with the fast charging/discharging double-layer capacitance and excellent mechanical properties of the carbon nanotubes. The electrochemically co-deposited composites are the most homogeneous and show an unusual interaction between the polymer and nanotubes, giving rise to a strengthened electron delocalisation and conjugation along the polymer chains. As a result they exhibit excellent electrochemical charge storage properties and fast charge/discharge switching, making them promising electrode materials for high power supercapacitors.