This contribution deals with the state of the art of studies concerning the fabrication of electric double-layer capacitors (EDLCs) also called super- or ultracapacitors and obtained using carbon nanotubes (CNTs) without exploiting Faradic reactions. From the first work published in 1997, EDLCs fabricated using carbon nanotubes as constitutive material for electrodes showed very interesting characteristics. It appeared that they could potentially outperform traditional technologies based on activated carbon. Different methods to fabricate the CNT-based electrodes have been proposed in order to improve the performances (mainly energy densities and power densities), for example filtration, direct growth on metal collector or deposition using an air-brush technique. In this contribution we will introduce the main works in the field. Finally, we will point out an emerging interest for supercapacitors fabricated on flexible substrates, exploiting the outstanding mechanical performances of CNTs, for new kinds of applications such as portable electronics.