Polymer nanocomposites have become a rich area of research due to their numerous applications and highly tunable properties. The heterogeneous length-scales present in polymer nanocomposites makes understanding microscopic details using macroscopic experiments a difficult task. Therefore, computational methods have been employed to investigate these materials at the molecular level. In this dissertation, I use computational methods to examine the phase behavior and infiltration kinetics of polymer nanocomposites. Working with experimentalists, these simulations give insight into the underlying molecular origins of material properties, which can drive more efficient design of polymer nanocomposites for specific applications. Using molecular dynamics and field-theoretic simulations, I examine two distinct polymer nanocomposite systems in detail. First, I replicate the conditions of systems generated via the experimental CaRI method using self-consistent field theoretic (SCFT) simulations. With these simulations, I analyze the thermodynamic phase behavior of both polymer blends and block copolymers under extreme nanoconfinement and asymmetric polymer-nanoparticle wetting conditions. I also replicate CaRI-produced composites using molecular dynamics (MD) simulations to study the dynamic infiltration properties of homopolymers, block copolymers, and random copolymers into confined nanoparticle packings. Secondly, I replicate conditions of systems generated using the polymer-infiltrated nanoporous gold method shown in using MD simulations. With these simulations, I analyze the infiltration dynamics ofpolymers into nanoporous gold scaffolds with varied confinement ratios and strengths of polymer-gold interaction.