Mechanics has historically played a pivotal role in science by providing the basis for classical physics. Today, with the advent of nanoscale mechanical devices combined with quantum electronic devices, we are witnessing a renaissance in the field of mechanics. After an introduction on the mesoscopic physics of nanomechanical resonators, I will discuss our recent advances on mechanical resonators based on carbon nanotubes. The nanotube in these devices vibrates as a guitar string. Single-electron tunneling enables coupling the mechanical vibrations to electrons by a large amount. I will show how to use this coupling to create a nonlinear mechanical oscillator approaching the quantum regime, where the resulting quantum energy levels of the mechanical oscillator are no longer evenly spaced. Using mechanical nanotubes hosting multiple quantum dots, we expect that our approach may enable the realization of a mechanical qubit and a quantum simulator of quantum matters featuring strong electron-phonon correlations.