The addition of nanoparticles (NPs) to a polymer matrix, forming a polymer nanocomposite (PNC), can extend and control macroscopic material properties. Many macroscopic properties (e.g. mechanical strength and small molecule transport) are dictated by microscopic dynamic processes, including dynamics of the polymer segments, chains, and NPs. Because the NPs and polymers have overlapping characteristic length, time, and energy scales, the interactions within these materials are complex, the dynamics are interrelated, and both remain poorly understood. Developing a fundamental and mechanistic understanding of polymer and NP dynamics in PNCs will lead to new opportunities, new innovations, and improved manufacturability, all of which may accelerate their universal introduction to society. This dissertation aims to navigate the hierarchy of dynamics in model PNCs. At the smallest length scale, we show that polymer segmental dynamics are slowed by the addition of highly-attractive, immobile NPs, particularly at the NP-polymer interface, and depend only weakly on temperature and matrix molecular weight. Despite measurable reductions in the timescale of motion, we show that the segmental diffusion process is mechanistically similar in PNCs and bulk. At longer length and timescales, we use molecular dynamics simulations to study chain-scale conformations and diffusion near confining athermal NPs. We show polymer diffusion is perturbed at longer length-scales than conformations and identify slow diffusion through confining NPs but bulk-like diffusion away from them. Using model attractive PNCs, we develop and demonstrate ion scattering measurements to extract the fraction of chains bound to the immobile NPs. These measurements show that the slow segmental relaxations at the interface persist to the chain-scale and reveal slow bound polymer desorption that occurs more readily at higher temperatures, lower polymer molecular weight, and longer times. Finally, we sample multiple length and timescales in mixtures of entangled polymer and very small, attractive NPs. We present experimental support of vehicular diffusion of NPs, which produces anomalously fast NP motion and commensurate slowing of polymer segments and polymer chain diffusion. Finally, we present X-ray photon correlation spectroscopy measurements of NP dynamics, small-angle neutron scattering measurements of the bound polymer layer in solution, and protocols for NP surface functionalization.