Abstract: Nanostructured carbon materials show a tremendous variety in atomic structure, morphology, properties, and applications. As all properties are ultimately determined by the structure of the material, a thorough understanding of the growth mechanisms that give rise to the particular structure is critical. On many occasions, it has been shown that plasma enhanced growth can be strongly beneficial. This review will describe the authors current understanding of plasma enhanced growth of carbon nanotubes, the prototypical example of nanostructured carbon materials, as obtained from experiments, simulations, and modeling. Specific emphasis is put on where experiments and computational approaches correspond, and where they differ. Also, the current status on simulating PECVD growth of some other carbon nanomaterials is reviewed, including amorphous carbon, graphene, and metallofullerenes. Finally, computational challenges with respect to the simulation of PECVD growth are identified.