Graphene has emerged as a subject of enormous scientific interest due to its exceptional electron transport, mechanical properties, and high surface area. When incorporated appropriately, these atomically thin carbon sheets can significantly improve physical properties of host polymers at extremely small loading. We first review production routes to exfoliated graphite with an emphasis on top-down strategies starting from graphite oxide, including advantages and disadvantages of each method. Then solvent-and melt-based strategies to disperse chemically or thermally reduced graphene oxide in polymers are discussed. Analytical techniques for characterizing particle dimensions, surface characteristics, and dispersion in matrix polymers are also introduced. We summarize electrical, thermal, mechanical, and gas barrier properties of the graphene/polymer nanocomposites. We conclude this review listing current challenges associated with processing and scalability of graphene composites and future perspectives for this new class of nanocomposites.