Abstract: The thermal vibration is the inherent vibration of nanostructures, which plays an important role in the dynamics of nanostructures. The quantum effects, the boundary effects and the van der Waals interaction have a significant influence on the thermal vibration of nanostructures. The carbon nanotubes and the graphene were extensively studied for their novel electronic properties and superior mechanical strength. This paper reviews some research methods for the thermal vibration of nanostructures, the thermal vibration of the carbon nanotube and the graphene in low temperatures and the nonlinear thermal vibration of the carbon nanotube.