The controlled synthesis of materials by methods that permit their assembly into functional nanoscale structures lies at the crux of the emerging field of nanotechnology. Although only one of several materials families is of interest, carbon-based nanostructured materials continue to attract a disproportionate share of research effort, in part because of their wide-ranging properties. Additionally, developments of the past decade in the controlled synthesis of carbon nanotubes and nanofibers have opened additional possibilities for their use as functional elements in numerous applications. Vertically aligned carbon nanofibers (VACNFs) are a subclass of carbon nanostructured materials that can be produced with a high degree of control using catalytic plasma-enhanced chemical-vapor deposition (C-PECVD). Using C-PECVD the location, diameter, length, shape, chemical composition, and orientation can be controlled during VACNF synthesis. Here we review the CVD and PECVD systems, growth control mechanisms, catalyst preparation, resultant carbon nanostructures, and VACNF properties. This is followed by a review of many of the application areas for carbon nanotubes and nanofibers including electron field-emission sources, electrochemical probes, functionalized sensor elements, scanning probe microscopy tips, nanoelectromechanical systems (NEMS), hydrogen and charge storage, and catalyst support. We end by noting gaps in the understanding of VACNF growth mechanisms and the challenges remaining in the development of methods for an even more comprehensive control of the carbon nanofiber synthesis process.