Understanding noncovalent interactions on the surfaces of carbon nanostructures (CNSs) is of fundamental importance and also has implications in nano- and biotechnology. The interactions of aromatic compounds such as benzene, naphthalene, and aromatic amino acids with CNSs of varying diameter, chirality, and curvature were systematically explored by using density functional theory. Planar graphene exhibits stronger binding affinity than curved carbon nanotubes (CNTs), whereas zigzag CNTs appear to show stronger binding affinity than armchair CNTs. For hydrocarbons, there exist two competing modes, namely, π–π stacking interactions and CH⋅⋅⋅π interactions, which bring the aromatic motifs into parallel and perpendicular dispositions with respect to the CNSs, respectively. Our results reveal that π–π stacking interactions override CH⋅⋅⋅π interactions in such cases. However, in the case of aromatic amino acids, π–π interactions can exist simultaneously along with a range of other interactions, including CH⋅⋅⋅π. The polarizability and HOMO energy of the CNSs were found to be the key factors that determine the binding energies. The HOMO–LUMO energy gaps of the CNSs were found to be undisturbed by the noncovalent functionalization of the aromatic molecules.