Phonon, a quantized lattice vibration, plays an important role in the materials’ physical and mechanical properties. This makes investigations on phonon dynamics an indispensable subject for better understanding the physical world. For decades, people have been seeking ways to manipulate phonon dynamics, which are closely related to atomic structures and electromagnetic properties of materials, for the development of novel materials with desired properties and more insights into the fundamental physics. This dissertation discusses the studies of phonon engineering in the spatially confined silicon systems, which have been widely used in the biomedical filed and have great potential applications in optoelectronic industry, as well as bulk sapphire systems using inelastic neutron scatterings.The dissertation starts with introducing the basic information about the phonon dynamics and neutron scatterings which are the two primary subjects of my graduate research. In Chapters 2 to 4, the inelastic neutron scattering experiments and discussions on the effects of particle size, temperature, surface oxidization, and surface functionalization on the phonon dynamics of silicon nanocrystals are presented. These effects are found to be greater on the transverse acoustic phonon modes than the optical phonon modes in silicon nanocrystals. In Chapter 5, the atomic structures of 3-nm spherical silicon nanocrystals were measured with elastic neutron scattering for the first time. The diffraction spectra show huge anisotropic structure variations inside the silicon nanocrystals compared to their bulk counterpart. In Chapter 6, the effect of the low concentration dopants on the phonon dynamics of sapphire was studied using inelastic neutron scattering. This dissertation sheds light on the phonon dynamics, as well as their dependence on the intrinsic and extrinsic effects, of materials with great potential applications and will contribute to further investigations on the phonon engineering of various materials.