Over the past several decades the use of polymers in applications such as microelectronics fabrication and nanocomposite materials has steadily increased. In these applications polymer chains are often confined to length scales comparable to their size. While it is well known that these confining environments alter polymer properties, a generalized understanding of how different confining geometries alter polymer behavior has not been established. Here we investigate changes to polymer conformation and diffusion under cylindrical and planar confinement using a combination of computational and experimental techniques. Using molecular dynamics simulations of polymer melts, we systematically examine changes in the polymer radius of gyration, shape anisotropy, and entanglement network under geometric confinement for a range of polymer chain sizes and confinement lengths. We found that conformational changes in confined polymers follow similar trends in cylindrical and planar confinement, though changes are more pronounced in cylindrical confinement. Conversely, measurements of polymer diffusivity show distinctly different behavior in the two geometries, with diffusivity in planar confinement increasing continuously with increasing confinement while in cylindrical confinement polymer diffusion is nonmonotonic, initially increasing then decreasing. The results of these simulations are compared to experimental measurements of polymer diffusion in anodic aluminum oxide nanopores over a range of temperatures using elastic recoil detection (ERD). The ERD measurements indicate slower diffusion in confinement for all temperatures, with greater changes observed at higher temperatures. These results differ from the simulation measurements, most likely due to differences in the starting conditions of the systems (i.e., polymers starting inside the pore in simulations versus outside the pores in experiments). Finally, we used small angle neutron scattering (SANS) and dynamical theory analysis (DTA) to investigate polymer conformation under planar confinement using a unique confining template that enables measurements of polymer conformation in confined and unconfined directions simultaneously. While the DTA model could reproduce the scattering from an empty channel template, the polymer scattering was too weak to isolate from the overall scattering pattern using the current template design. Single component templates and contrast matched polymers are necessary to reduce the scattering contributions from the template and to better isolate polymer scattering.