We have investigated the noncovalent interactions in carbohydrate-aromatic interactions which are pivotal to the recognition of carbohydrates in proteins. We have employed quantum mechanical methods to study carbohydrate-aromatic complexes. Due to the importance of dispersion contribution to the interaction energy, we mainly use density functional theory augmented with an empirical correction for the dispersion interactions (DFT-D). We have validated this method with a limited number of high level ab initio calculations. We have also analysed the vibrational and NMR chemical shift characteristics using the DFT-D method. We have mainly studied the complexes involving β-glucose with 3-methylindole and p-hydroxytoluene, which are analogues of tryptophan and tyrosine, respectively. We find that the contribution for interaction energy mainly comes from CH/π and OH/π interactions. We find that the interaction energy of complexes involving CH/π and OH/π interactions is reflected in the associated blue and red shifts of vibrational spectrum. We also find that the interactions involving 3-methylindole are somewhat greater than those for p-hydroxytoluene. The C-H blueshifts are also in parallel with the predicted NMR proton shift. We have also tested different density functionals including both standard density functionals and newly developed M0x functionals and MP2 method for studying carbohydrate-aromatic complexes. The DFT-D method and M06 functionals of the M0x family are found to perform better, while B3LYP and BLYP functionals perform poorly. We find that the inclusion of a dispersion term to BLYP is found to perform better. The dispersion energy dominates over the interaction energy of carbohydrate-aromatic complexes. From the DFT-D calculations, we found that the complexes would be unstable without the contribution from dispersive energy. We have also studied the importance of noncovalent interactions in functionalization of nanotubes by nucleic acid bases and aromatic amino acids by using semi-empirical methods with dispersion term such asPM3-D and PM3-D*. We find that the both semi-empirical schemes give reasonable interaction energies with respect to DFT-D interaction energies. We have also used PM3-D method to study the adsorption of organic pollutants on graphene sheet and on nanotubes. We found that the semi-empirical schemes, which are faster and cheaper, are suitable to study these larger molecules involving noncovalent interactions and can be used as an alternative to DFT-D method. We have also studied the importance of dispersion interaction and the effect of steric hindrance in aggregation of functionalized anthracenes and pentacenes. We have also employed molecular dynamics simulation methods to study the aggregation of anthracene molecules in toluene solution.