Nanomechanical resonators are used with great success to couple mechanical motion to other degrees of freedom, such as photons, spins and electrons. The motion of a mechanical eigenmode can be efficiently cooled into the quantum regime using photons, but not other degrees of freedom. Here, we demonstrate a simple yet powerful method for cooling, amplification and self-oscillation using electrons. This is achieved by applying a constant (d.c.) current of electrons through a suspended nanotube in a dilution refrigerator. We demonstrate cooling to 4.6 ± 2.0 quanta of vibrations. We also observe self-oscillation, which can lead to prominent instabilities in the electron transport through the nanotube. We attribute the origin of the observed cooling and self-oscillation to an electrothermal effect. This work shows that electrons may become a useful resource for cooling the mechanical vibrations of nanoscale systems into the quantum regime.