The chemical production of graphene as well as its controlled wet chemical modification is a challenge for synthetic chemists. Furthermore, the characterization of reaction products requires sophisticated analytical methods. In this Review we first describe the structure of graphene and graphene oxide and then outline the most important synthetic methods that are used for the production of these carbon-based nanomaterials. We summarize the state-of-the-art for their chemical functionalization by noncovalent and covalent approaches. We put special emphasis on the differentiation of the terms graphite, graphene, graphite oxide, and graphene oxide. An improved fundamental knowledge of the structure and the chemical properties of graphene and graphene oxide is an important prerequisite for the development of practical applications.