Abstract: Thermal transport in nanoscale structures has attracted an increasing attention in last two decades. Here we give a brief review of the recent developments in experimental and theoretical studies of heat transport in nano materials such as nanotube and nanowire. In particular, we will demonstrate that the phonons in nanotube and nanowires transport super-diffusively, which leads to a length dependent thermal conductivity. In other words, heat conduction in low dimensional nanostructures does not obey the Fourier’s law.