Carbon nanotube (CNT) yarn, consisting of 23 µm diameter CNT filaments, can be used as capacitive electrodes that are long, flexible, conductive and strong, for applications in energy and electrochemical water treatment. We measure the charge storage capacity as function of salt concentration, and use Gouy–Chapman–Stern theory to describe the data. CNT yarn can also be used as conductive scaffold for the application of a porous activated carbon (AC) layer. We show the potential of CNT yarn for the generation of electrical energy from environmental entropy differences, by coating yarn (both with and without AC coating) with ion-exchange membranes (IEMs) and generating power from the salt concentration difference between river water and seawater. The use of flexible and conductive CNT yarns as capacitive electrodes and electrode scaffolds breaks with the paradigm of planar static electrodes, and opens up a range of alternative designs for electrochemical cells with enhanced performance.