Graphene based nanostructured systems comprise a material class of growing technological and scientific importance. Joining materials with vastly different properties, polymer graphene heterosystems promise diverse applications in surface and nanotechnology, including, for example, thin films, nanocomposites, organic photovoltaics or nanotribology. Here we present results from a molecular simulation approach for the detailed study of hybrid graphene/polymer materials at the molecular level, over a broad range of time and length scales. Results concerning structure-properties relations are presented, for various hybrid multi-phase systems: (a) Thin polymer films supported by multi-layer graphene sheets, (b) Graphene based polymer nanocomposites with different types of functionalized graphene layers, and (c) Crystallization and ultra-fast melting of a single polymer chain adsorbed on freestanding graphene. The spatial and dynamical heterogeneities of the hybrid systems are analyzed, resolving their effect on the structural and dynamical (Brownian motion) behavior of both polymer chains and graphene layers.