Abstract: This thesis discusses electrical and thermal transport measurements on C₆₀, carbon nanotubes, and boron-nitride nanotubes. Chapter 1 describes the anomalous resistivity behavior of Ag films on C₆₀ crystals. The correlation of the resistivity anomaly and the structural phase transition is established. Chapter 2 gives an introduction to the physical properties and the synthesis methods of carbon and boron nitride nanotubes. Chapter 3 shows two different approaches on chemical functionalization of boron-nitride nanotubes. Chapter 4 gives the theoretical background of thermal conductivity, especially for nano-structured materials. A summary of theoretical and experimental works on the thermal conductivity of nanotubes is given. Chapter 5 discusses the experimental results of thermal conductivity of nanotube mats. An absolute value of the thermal conductivity of boron nitride nanotubes is bracketed and can be compared to the results of the following chapters on individual nanotubes. Chapter 6 describes the experimental methods of measuring thermal conductivity of individual nanotubes. Chapter 7 shows the 2 temperature dependent thermal conductivity and thermopower of individual nanotubes. Chapter 8 discusses the isotope effect and the diameter dependence of the thermal conductivity of nanotubes. In chapter 9, it is shown that the thermal conductivity of nanotubes is robust against electron irradiation and structural deformation. Importantly, the observation challenges current understandings on the thermal transport of nano-structured materials. In chapter 10, it is shown that it is possible to reversibly tune the thermal conductivity of a multiwalled nanotube by controllably sliding the outer-shells against inner cores. Chapter 11 describes a thermal rectifier by engineering the mass distribution along a nanotube. The observed non-zero thermal rectification effect provides strong evidence for solitons in nanotubes. The soliton model also coherently explains many phenomena described in chapter 10 and chapter 12. In chapter 12, it is shown that Fourier's law is violated in nanotubes and the observed anomalous heat transport is consistent with the soliton model. The significance of these discoveries can provide new thoughts for current thermal management problems. Based on these results, it is proposed to utilize phonons as information carriers.