Nanotube (such as carbon and boron nitride nanotubes) is a key component of modern technology applications of nanostructures due to their unique mechanical, electrical, and physical characteristics such as high elasticity modulus, suitable heat transfer, and electrical conductivity. Carbon and boron nitride nanotubes are among the promising choices in nano-fluidic, gas storage, and drug delivery systems due to their hollow cylindrical shape and appropriate chemical, mechanical, and physical properties. Thermal vibration assessment should be conducted on fluid-conveying carbon nanotubes since the effect of thermal fluctuations on the mechanical characteristics of nanostructure are significant. Previous studies have revealed that when thermal vibration is taken into account, quantum effects can become extremely important in nanoscale electronics and structures. Hence, the present review focuses mostly on previous work on fluid-conveying nanotubes and the dynamical characteristics of size-dependent vibration and non-local strain gradient theory of fluid-conveying nanotubes. Furthermore, a special effort is made to address recent and rare investigations on the vibration of fluid-conveying nanotubes in thermal environment, as well as thermal vibration concerns of carbon nanotubes.