Nanometer-sized particles that are well dispersed in a polymer melt, presumably due to strongly favorable particle-polymer interactions, can form fractal structures via polymer bridging, leading ultimately to a nanoparticle (NP) network analogous to a colloidal gel. The linear viscoelastic response of polymer nanocomposites can be quantitatively predicted by a parameter-free model in which the stress is a simple sum of contributions from the polymer matrix and the fractal NP structure linked by bridging polymer chains. The NP contribution is modeled using critical percolation, while the polymer part is enhanced by the presence of particles, owing to hydrodynamic interactions. The phase diagram at the right shows that small NPs are needed to achieve the stronger reinforcement from glassy bridges at reasonable particle loadings.