We report the results of coarse-grained simulations of the transport of penetrants in polymer nanocomposite materials. This work was motivated by recent experimental results in the context of conductivity and barrier properties of polymer nanocomposites. We adopt a coarse-grained simulation formalism which is suitable for studying issues surrounding the transport of ions, large gas molecules and probes in polymer nanocomposite systems. The results presented focuses on two issues: (i) the role of polymer interfacial layers and (ii) the influence of polymer matrix dynamics upon the transport properties of polymer-nanoparticle mixtures. Our results indicate that in our model the penetrant transport properties are dominated by the "filler" effect, in which the particles act as obstructions for the penetrant diffusion. Interfacial effects, which are driven by the polymer-particle interactions play a role, but their impact is shown to be less important than the filler effect. A second outcome of our work is a demonstration that matrix segmental dynamics play a very important role in determining the overall transport properties of the PNC. For nanoparticle systems, such effects are shown to lead to significant deviations from continuum mechanical theories for the effective properties of particulate dispersions.