Carbon nanomaterials, including carbon nanotubes and graphene, with various unique physical and chemical properties are emerging as extraordinary materials for biomedical applications. The aim of this thesis was to functionalise single walled carbon nanotubes and reduced graphene oxide with range of biomolecules including, peptides, peptoids, and ribonucleosides. The first study investigated the noncovalent interaction between single walled carbon nanotubes and fluoro tagged nano-1 peptide with 19F NMR. In the second study single walled carbon nanotubes were noncovalently functionalised with a series of antibacterial, chiral, amphiphilic peptoids. The peptoids varied in the number of aromatic residues on the hydrophobic surface of the helix. It was found that peptoid’s ability to individually disperse single walled carbon nanotubes increased with increasing the number of aromatic residues. The third study presented the first experimental noncovalent interaction of ribonucleosides, nucleobases, and ribose with purified and oxidised single walled carbon nanotubes. It was found that cyclic and aromatic ribonucleosides and nucleobases are too small to disperse the hydrophobic nanotube surface by π-π stacking. Furthermore, results showed that the ribonucleosides dispersion ability towards nanotubes depends on the number of oxygen-containing functional groups on the nanotube surface. In the final research it was found that the flat rigid surface of reduced graphene oxide has a critical role in its noncovalent interaction with peptides and peptoids. Results showed that biomolecules with higher backbone flexibility can give a higher dispersion affinity towards reduced graphene oxide. Also, it was found that ribonucleosides and their nucleases, and ribose moieties have very limited dispersion affinity towards reduced graphene oxide. Finally, the covalent functionalisation of reduced graphene oxide with cell penetrating peptoid, thymidine, and adenosine was investigated.