This dissertation presents thermal and thermoelectric measurements of nanostructures. Because the characteristic size of these nanostructures is comparable to and even smaller than the mean free paths or wavelengths of electrons and phonons, the classical constitutive laws such as the Fourier’s law cannot be applied. Three types of nanostructures have been investigated, including nanoscale constrictions patterned in a sub-100 nm thick silicon film, monatomic thick graphene ribbons supported on a silicon dioxide (SiO₂) beam, and indium antimonide (InSb) nanowires. A suspended measurement device has been developed to measure the thermal resistance of 48-174 nm wide constrictions etched in 35-65 nm thick suspended silicon membranes. The measured thermal resistance is more than ten times larger than the diffusive thermal resistance calculated from the Fourier’s law. The discrepancy is attributed to the ballistic thermal resistance component as a result of the smaller constriction width than the phonon-phonon scattering mean free path. Because of diffuse phonon scattering by the side walls of the constriction with a finite length, the phonon transmission coefficient is 0.015 and 0.2 for two constrictions of 35 nm x 174 nm x220 nm and 65 nm x 48 nm x 50 nm size. Another suspended device has been developed for measuring the thermal conductivity of single-layer graphene ribbons supported on a suspended SiO₂ beam. The obtained room-temperature thermal conductivity of the supported graphene is about 600 W/m-K, which is about three times smaller than the basal plane values of high-quality pyrolytic graphite because of phonon-substrate scattering, but still considerably higher than for common thin film electronic materials. The measured thermal conductivity is in agreement with a theoretical result based on quantum mechanical calculation of the threephonon scattering processes in graphene, which finds a large contribution to the thermal conductivity from the flexural vibration modes. A device has been developed to measure the Seebeck coefficients (S) and electrical conductivities ([sigma]) of InSb nanowires grown by a vapor-liquid-solid process. The obtained Seebeck coefficient is considerably lower than the literature values for bulk InSb crystals. It was further found that decreasing the base pressure during the VLS growth results in an increase in the Seebeck coefficient and a decrease in the electrical conductivity, except for a nanowire with the smallest diameter of 15 nm. This trend is attributed to preferential oxidation of indium by residual oxygen in the growth environment, which could cause increased n-type Sb doping of the nanowires with increasing base pressure. The deviation in the smallest diameter nanowire from this trend indicates a large contribution from the surface charge states in the nanowire. The results suggest that better control of the chemical composition and surface states is required for improving the power factor of InSb nanowires. On approach is to use Indium-rich source materials for the growth to compensate for the loss of indium due to oxidation by residual oxygen. / text