Nanoparticle - polymer composites, or polymer nanocomposites, are ubiquitous in the modern world. Controlled dispersion of nanoparticles in nanocomposites is often a critical requirement and has lead to evolution of a variety of strategies for regulating nanoparticle interactions and assembly. This work focuses on one such technique wherein the nanoparticle surfaces are densely tethered with polymer chains. Complete screening of the interparticle interactions and steric repulsion among the tethered chains thus results in repulsive and stable nanoparticles across a range of polymer molecular weights and chemistries and nanoparticle volume fraction. These nanoparticles are found to be ideal for studying polymer nanocomposites, and a phase diagram constructed on the basis of nanoparticle arrangements is presented. Tethered nanoparticles, in the limit small tethered polymer chains, also serve as model systems for studying the properties of soft nanoparticles. Well-dispersed suspensions of these soft nanoparticles in oligomers exhibit unique properties across the jamming transition, including anomalous structural and dynamic trends typically associated with complex molecular fluids. In the jammed regime, these suspensions behave as typical soft glasses and allow for quantitative comparisons with the existing models for soft glasses. At the same time, the tethered chains facilitate relaxations even in the deeply jammed regime and thus lead to novel features including Newtonian behavior and terminal relaxations in the jammed suspensions. On the other end of the spectrum, studies of suspensions of these nanoparticles in extremely large polymer chains provide insights on the physical processes responsible for the atypical, negative non-Einsteinian deviations in the viscosity typically observed in blends of nanoparticles in large polymer hosts. We also explore the origins of atypical faster - than - diffusion relaxation mechanisms in soft materials through studying the relaxation mechanisms in these jammed suspensions as well as single-component tethered nanoparticle fluids. A simple theoretical framework is presented to account for the genesis of driving mechanisms in our systems, and comparisons between theoretical and experimental results provide strong support to the existing theory that hyperdiffusion in soft materials arises from the system's response to internal stresses; however, the origin of these internal stresses might vary considerably from one material to another.