Recent advances in the synthesis of inorganic and organic nanowires and nanotubes have provided both components for various functional devices and platforms for the study of low-dimensional transport phenomena. However, tremendous challenges have remained not only for the integration of these building blocks into functional devices, but also in the characterization of the fundamental transport properties in these nanoscale model systems. In particular, thermal and thermoelectric transport measurements can be considerably more complicated than electron transport measurements, especially for individual nanostructures. During the past decade, a number of experimental methods for measuring the thermal and thermoelectric properties of individual nanowires and nanotubes have been devised to address these challenges, some of which are reviewed and analyzed in this chapter. Although the Seebeck coefficient and electrical conductivity can also be obtained from some of the measurement methods, this chapter is focused on measurement techniques of the thermal conductivity and thermal diffusivity of nanowires and nanotubes. It is suggested that the limitations in the current experimental capability will provide abundant opportunities for innovative approaches to probing fundamental thermal and thermoelectric transport phenomena in individual nanostructures.