Comprehending the interplay between thermal conductivity and phonon dynamics in semiconductors and insulators holds significance for the field of phonon engineering. While substantial progress has been made in the theoretical understanding of this relationship over the last decade, many of these predictions lack empirical validation. This dissertation endeavors to bridge this experimental gap, focusing particularly on the validation of theoretical insights, with a special emphasis on boron arsenide (BAs), a recently discovered material exhibiting ultrahigh thermal conductivity.Temperature-induced changes in phonon occupation impact thermal conductivity, making it a valuable probe for understanding phonon scattering in materials. Through systematic investigations of BAs samples across the temperature range of 300 to 600 K, we discovered a more pronounced temperature dependence (1/T^2) than theoretical predictions (1/T^1.7) in BAs sample with ambient thermal conductivity of 1500 W m-1 K-1. This discrepancy indicates that existing calculations have underestimated the importance of four-phonon scattering in BAs. Pressure renders a systematic tool to modulate phonon dispersion, offering insights into the correlation between changes in phonon dispersion and thermal conductivity. The Leibfried-Schlömann (LS) equation, a phenomenological model known for its predictive capabilities, has been successfully applied to elucidate the pressure dependence of thermal conductivity in numerous materials. My initial investigations focused on two perovskites, SrTiO3 and KTaO3, revealing that their thermal conductivity variations align with LS equation predictions. The distinct pressure sensitivities observed in SrTiO3 and KTaO3 underscore the pivotal role of phonon lifetime in determining pressure-induced alterations in thermal conductivity. However, when applying the LS equation to BAs, a notable discrepancy emerged. While the LS equation projected a threefold increase in BAs’s thermal conductivity at 30 GPa, our experimental findings demonstrated much less changes. Subsequently, I extended my investigations to GaN, which shares certain phonon dynamics similarities with BAs. Both BAs and GaN have a frequency gap in their phonon dispersion. GaN exhibited a stronger pressure dependence, aligning well with LS equation predictions. Furthermore, I conducted pressure-dependent measurements on diamond, where my data exhibited acceptable agreement with LS predictions. This comparative analysis among BAs, GaN, and diamond underscores the distinctive thermal characteristics of boron arsenide.