A carbon nanotube (CNT) is a remarkable material and can be thought of as a single-atom thick cylinder of carbon atoms capped of with a semisphere. This is called a single-walled CNT and, depending on how the cylinder is rolled up, CNTs are either semiconducting or metallic. A CNT is made into a mechanical resonator by suspending it between two electrodes. The CNT is driven into motion electrostatically, and the mechanical motion is detected using the current flowing through the CNT. We use the ultraclean fabrication method, which avoids processing on the CNT by first making the electrodes and the trench and only in the final step growing the CNTs. A suspended CNT resonator can be fabricated without defects, thus reducing mechanical damping. In this Thesis, CNTs are studied as electromechanical resonators. An overview is given of the various optical, microscopy, and electrical methods to detect the mechanical motion of CNT resonators, after which the electrical detection methods are compared in detail. Next, it is shown experimentally and theoretically that their mechanical motion couples strongly to single-electron tunneling, as CNTs become quantum dots at cryogenic temperatures. Mechanical modulation of the single-electron average charge leads to spring softening, damping, and a nonlinear restoring force. Because of their high aspect ratio, CNTs can easily be perturbed into the nonlinear regime. To read out their mechanical motion at high frequencies, a novel high-bandwidth readout scheme is developed and discussed.