We use coarse-grained computer simulations to delineate the mechanisms governing the linear viscoelasticity and the steady-shear rheology of polymer nanocomposites. Our studies specifically focus on the regimes where the particle sizes and the interparticle distances become comparable to the polymer sizes and where the interactions between polymer and particles become relevant in influencing the dynamical characteristics. Our results suggests the rheology of polymer nanocomposites are very similar to that of colloidal suspensions in a simple fluid when polymer rheology, the particle-induced changes in the polymer rheology and the polymer slip effects are accounted. Using our results we suggest how a simple model can be constructed for the rheological behavior over the entire range of volume fractions of the nanofillers. Our results and mechanistic explanations are in very good agreement with associated experimental observations.