In the solar energy, thermoelectric, and solid-state laser industries, polycrystalline semiconductors and ceramics have been widely researched and applied to integrated devices. While the thermal conductivity (k) of single crystals has been well-studied, k of polycrystalline materials is attracting more attention because it varies a lot with different processing techniques, alloying, impurities, porosity, and microstructures. As nanotechnology causes an evolution in the state of the art materials, researchers are also becoming interested in using nanostructuring to engineer properties including k in these materials with nano-scale grains.

This thesis investigates the thermal conductivity of some representative bulk polycrystalline semiconductors (Si, Si_1-xGe_x, and Mg₂Si_1-xGe_x) and ceramics (Al₂O₃ and AlN) used for different applications. The samples are made by collaborators using a current activated, pressure assisted densification (CAPAD) method. The k of these samples is measured by the 3&omega method and analyzed using kinetic theory and Matthiessen's rule. For pure Si, the importance of grain size and pores on k is emphasized. A revised frequency-dependent (non-gray) model is proposed to better describe the phonon scattering mechanism at grain boundaries. For Si_1-xGe_x, the impact of homogeneity on k is observed. For Mg₂Si_1-xGe_x, the combined effects of alloy scattering and grain boundary scattering are discussed because they can potentially benefit the search for high efficiency thermoelectric devices. For Al₂O₃ and AlN, the method of preparation of powers and additives are observed to have profound effect on k, due to segregation at grain boundaries, and this can be tuned to give much better thermal performance for high power laser applications as compared to current Nd:YAG based devices.