This article provides a comprehensive review about the use of nonlocal theory in modeling of the vibrations of the carbon nanotube resonators. It is fully described how the nonlocal effect has been exploited by researchers to mathematically model vibrations of carbon nanotube resonators. Fusion of different classical beam theories with nonlocal theory is discussed. Also, the article presents the combination of nonlocal models with different physical phenomena which have influence in the vibrations of carbon nanotube resonators.