Polymer nanocomposites have been a topic of interest in recent years for their potential in applications such as water desalination, CO2 capture, photovoltaics, battery membranes and immersion lithography. Unlike colloids which tend to agglomerate irreversibly, polymer grafted colloids are stabilized by polymer-polymer steric interactions. Polymer grafted nanoparticles(PGNs) are a class of such materials which consist of an inorganic nanoparticle core, functionalized with a corona of organic oligomers. These differ from common nanocomposites in that the tethered corona can be used as the sole suspending medium for the cores. The hybrid nature of the suspension allows the fabrication of materials with tunable properties by varying parameters such as nanoparticle chemistry, shape and size, as well as the polymer molecular weight, grafting density and chemistry. The range of properties exhibited by these composites vary from solids, stiff waxes, and gels for high core content to single component solvent free fluids for low core content. While PGNs have been extensively studied experimentally by several groups at Cornell, this research focuses on the use of molecular simulations to help elucidate the effect of molecular design on the properties of PGNs. We studied the effect of grafting density, corona thickness and core volume fraction on equilibrium and non-equilibrium properties like diffusivity, rotational diffusivity, equilibrium structure, rheology and molecular origin of stress. We find that increasing the chain length and grafting density decreases the viscosity and structural order, which makes the system to have a more liquid-like behavior. While these trends have also been observed in experiments and predicted by analytical theories, our results complement simulations data from other groups to provide a molecular basis for these phenomena and to create phase diagrams to encapsulate the behavior of a large number of systems. We also compare the properties of solvent-free PGNs with those suspended in a solvent, and examine the effect of dilution in these systems. We find that solvent-free systems have higher viscosity and a larger shear thinning coefficient. On studying the phase behavior of PGNs in chemically identical polymeric solvents, we find that changing the ratio of polymer length to nanoparticle size can result in a transition from well-mixed systems to phase-separated systems, a phenomenon that could be attributed to the interplay between entropic forces acting on the grafted and free polymers. Our simulations reveal trends in structural packing for low curvature PGNs that are consistent with those observed in experiments and predicted by theory (e.g., as pertaining to the first peak of structure factor), while predicting that for high curvature PGNs macrophase separation can occur (a trend yet to be tested experimentally).