The discovery of graphene and carbon nanotubes (rolled-up graphene) has excited the world because their extraordinary properties promise tremendous developments in many areas. Like any materials with application potential, it needs to be fabricated in an economically viable manner and at the same time provides the necessary quality for relevant applications. Graphene and carbon nanotubes are no exception to this. In both cases, chemical vapor deposition (CVD) has emerged as the dominant synthesis route since it is already a well-established process both in industry and laboratories. In this work, we review the CVD fabrication of graphene and carbon nanotubes. Initially, we briefly introduce the materials and the CVD process. We then discuss pretreatment steps prior to the CVD reaction. The discussion then switches to the CVD process, provides comparative data for thermal CVD and plasma-enhanced CVD, and includes coverage of kinetics, thermodynamics, catalyst choice, and other aspects of growth as well as post production treatments. Finally, conclusions are drawn and presented.