Can you imagine a material that is many times stronger than steel, yet flexible when bent or twisted, that withstands ultrahigh heat, and that conducts heat better than diamond? Does this dream material really exist? Yes. "Carbon nanotubes." The excellent mechanical properties of nanotubes include an extremely high Young's modulus (ca. 1 TPa) and tensile strength (50 GPa or higher), whose values are several times higher than those of steel. Furthermore, since its specific gravity is less than one-tenth that of steel, it offers 100 times larger mechanical strength than steel with the same weight. Another characteristic of nanotubes is their extreme flexibility to bending and twisting deformation. It was experimentally confirmed that a nanotube returns to its original shape like a rubber hose even when the entire tube is twisted or bent until it is warped.In this contribution, we will give a comprehensive overview of the research progress to date, focusing on the mechanical properties of carbon nanotubes. The first half examines minute deformations in the elastic region; the latter half takes a closer look at the plastic deformation of nanotubes under extreme conditions including giant deformation, high temperature and pressure and electron beam irradiation.