Polymers have been used for variety of products for decades, and the usage of polymer products is still growing. Innovative methods (e.g. adding other materials) have been created to improve properties of polymer products to fulfill targeted requirements for applications and many of these strategies impose confinement on polymers. As nanotechnology and manufacturing technology advance, the confinement lengths keep shrinking and approaching the size of a single chain. While the final properties of polymer products are important for the applications, understanding how polymers behave at the microscopic scale is also critical for manufacturing and designing polymer products, especially when the manufacturing methods or the final states of polymers impose nano-confinement. To understand how polymers behave in nano-confinement, two main types of confinement are studied in this dissertation: polymer nanocomposites involving spherical and cylindrical nanoparticles and nanoconfinement directly imposed by impenetrable planar and cylindrical walls. Polymer structure can be affected when adding nanoparticles into polymer matrices, which may lead to a change in dynamics. Small angle neutron scattering is applied to study how polymer structure is affected by carbon nanotubes (CNTs). Polymer chains retain a Gaussian chain conformation, and the chain size expands (~ 30% for 10 wt% SWCNT loading) when the chain size (Rg) is larger than the radius of the filler (r) and the SWCNT mesh size is comparable to Rg. Chain expansion is not observed for MWCNT, where r ~ Rg. Moreover, when the SWCNT mesh is anisotropic the polymer conformation is anisotropic with greater expansion perpendicular to the SWCNT alignment, which is the direction with small mesh size. The temperature dependence of polymer tracer diffusion is investigated. In MWCNT/PS nanocomposites, a diffusion minimum is observed with increasing nanotube concentration at 7 temperatures from 152°C to 214°C. The diffusion minimum is shallower at higher temperature, which indicates the mechanism that slows polymer diffusion is less pronounced at higher temperatures. At fixed concentration the temperature dependence data fit the WLF equation. The temperature dependence of polymer tracer diffusion in silica/PS nanocomposites also obeys the WLF equation. However, the monotonic decrease of the tracer diffusion when silica concentration increases is more pronounced at higher temperature, which shows an opposite trend than the MWCNT/PS system. The thermal expansion coefficients of free volume (αf), obtained by fitting the temperature dependence data to the WLF equation, slightly increases when silica concentration increases. In contrast, the αf obtained from the time-temperature superposition of the rheology data decreases with silica concentration increases and shows an abrupt change at the percolation concentration of silica NPs. This finding suggests that the mechanical response of silica NPs contributes to the linear viscoelastic response. The impacts of nanoconfinement imposed by impenetrable planar or cylindrical walls were investigated by molecular dynamics simulations and experiments. The polymer conformation in thin film or cylindrical confinement is compressed parallel to the confining direction and slightly elongated perpendicular to the confining direction. The number of entanglement per polymer (Z) decreases as the pore diameter decreases. A theory, which assumes that the preferential orientation of the end-to-end vector can be directly transferred to the preferential orientation of primitive path steps, compares favorably to our simulations as a function of pore diameter. From the simulation, we also found that the local relaxation is accelerated along the cylindrical axis and is retarded perpendicular to the cylindrical axis. Combining the change in chain conformation, entanglement density, and the local relaxation, we found an increase for the center-of-mass polymer diffusion (Drep) in cylindrical confinement via the reptation model. The center-of-mass diffusion coefficients (DMSD) are also directly calculated from the mean-squared displacement in the diffusive regime, and are compared to Drep. At modest confinements, Drep agrees with DMSD, which suggests the applicability of the reptation model. At strong confinement, Drep > DMSD implies the limitations of the reptation model. The center-of-mass diffusion coefficient (Dexp) is also measured experimentally using diffusing deuterated polystyrene into porous anodized aluminum oxide membranes pre-infiltrated by polystyrene. As the pore diameter decreases Dexp increases in qualitative agreement with the molecular dynamics simulations (Drep and DMSD). The local relaxations of polymers in cylindrical confinement are measured experimentally using QENS. When polystyrene is confined in cylindrical nanopores, the segmental relaxations slow down non-monotonically with pore size. This trend is also observed for EISF, which measured the fraction of non-diffusing hydrogen within the probing time scale of QENS. At last, we found that when d/Ree > 2, hydrogen has the lowest MSD. When the pore size is decreasing to 2 > d/Ree > 1, MSD is slightly higher but still lower than that for bulk PS. When the pore size is further decrease to d/Ree < 1, MSD decreases again. This non-monotonic change of MSD can be explained by combining the effect of cylindrical confinement on the local segmental relaxation and non-diffusing hydrogen. This thesis provides the first study of polymer structure in polymer nanocomposites with high-aspect ratio nanoparticles and the first systematic computer simulation study for polymer confined in cylindrical confinements. These studies contribute to the understanding of the physics of confined polymers and correlations between changes in structure and dynamics.