The study of electrochemical behavior of bioactive molecules has become one of the most rapidly developing scientific fields. Biotechnology and biomedical engineering fields have a vested interest in constructing more precise and accurate voltammetric/amperometric biosensors. One rapidly growing area of biosensor design involves incorporation of carbon-based nanomaterials in working electrodes, such as one-dimensional carbon nanotubes, two-dimensional graphene, and graphene oxide. In this review article, we give a brief overview describing the voltammetric techniques and how these techniques are applied in biosensing, as well as the details surrounding important biosensing concepts of sensitivity and limits of detection. Building on these important concepts, we show how the sensitivity and limit of detection can be tuned by including carbon-based nanomaterials in the fabrication of biosensors. The sensing of biomolecules including glucose, dopamine, proteins, enzymes, uric acid, DNA, RNA, and H2O2 traditionally employs enzymes in detection; however, these enzymes denature easily, and as such, enzymeless methods are highly desired. Here we draw an important distinction between enzymeless and enzyme-containing carbon-nanomaterial-based biosensors. The review ends with an outlook of future concepts that can be employed in biosensor fabrication, as well as limitations of already proposed materials and how such sensing can be enhanced. As such, this review can act as a roadmap to guide researchers toward concepts that can be employed in the design of next generation biosensors, while also highlighting the current advancements in the field.