Graphene-based materials are single- or few-layer platelets that can be produced in bulk quantities by chemical methods. Herein, we present a survey of the literature on polymer nanocomposites with graphene-based fillers including recent work using graphite nanoplatelet fillers. A variety of routes used to produce graphene-based materials are reviewed, along with methods for dispersing these materials in various polymer matrices. We also review the rheological, electrical, mechanical, thermal, and barrier properties of these composites, and how each of these composite properties is dependent upon the intrinsic properties of graphene-based materials and their state of dispersion in the matrix. An overview of potential applications for these composites and current challenges in the field are provided for perspective and to potentially guide future progress on the development of these promising materials. Display omitted