In the last decade, the use of carbon nanotubes and graphenes has been on the rise for various nanobiotechnological applications. Owing to their special characteristics, these two nanostructures of carbon allotropes have been studied for their capacity in the detection and treatment of many diseases. On the other hand, curcumin, a well-known antioxidant and anticancer natural product, is being extensively studied for numerous medicinal applications. Interestingly, many reports have shown great potentials of conjugates of curcumin and carbon nanotubes or graphenes. These conjugates, when properly designed and functionalized with biomolecules, could represent the valuable properties of each component alone while they could be effective in overcoming the poor solubility issues of both curcumin and carbon nanomaterials (CNMs). In this case, curcumin conjugates with CNMs seem to be very promising in biosensing applications and the detection of many biomolecules, especially, curcumin has been reported to be very effective with these conjugates. Also the delivery of curcumin using functionalized SWCNTs was evaluated for its ability to load and release curcumin, to protect curcumin from degradation and to enhance its solubility. It is proposed that other properties of these conjugates are still to be discovered and the interdisciplinary approaches among biology, medicine, chemistry, and material engineering will accelerate the applications of these novel materials. This review aims to summarize the findings on the applications of CNM conjugates of curcumin.