The nanoscale graphene platelet (NGP) or graphene nanosheet is an emerging class of nanomaterials. An NGP is a nanoscale platelet composed of one or more layers of a graphene plane, with a platelet thickness from less than 0.34 to 100 nm. NGPs are predicted to have a range of unusual physical, chemical, and mechanical properties. Although practical electronic device applications for graphene are not envisioned to occur within the next 5-10 years, its application as a nanofiller in a composite material is imminent. The availability of processable graphene sheets in large quantities is essential to the success in exploiting composite and other applications. This review first describes the earlier processes for producing mostly multi-layer NGPs and their composites, which is followed by a discussion on the recent developments in the preparation of single-layer NGPs and their nanocomposites. Fundamental principles behind processing of nanographene materials are also briefly discussed.