Computational methods have been extensively developed at various levels of approximation in recent years to model biomolecular interactions and for rational drug design. This research work aims to explore the feasibility of using quantum mechanical (QM) methods within the two broad categories of in silico ligand-based and structure-based drug design. First, density functional theory at the M06L level of theory was employed to examine structure-activity relationships of boron-based heterocyclic compounds, anti-inflammatory inhibitors targetting the interleukin-1β (IL-1β) cytokine. Our findings from computed energies and shapes of the molecular orbitals provide understanding of electronic effects associated with the inhibitory activity. We also found that the boron atom, specifically its electrostatic polarity, appears to be essential for the anti-IL-1β activity as evidenced by the biological assay of non-boron analogues selected from the ligand-based virtual screening results. Secondly, we aimed to dock ligands at the active sites of zinc-containing metalloproteins with reasonable computational cost and with accuracy. Therefore, an in-house docking scheme based on a Monte Carlo sampling algorithm using the semiempirical PM6/AMBER force field scoring function was compiled for the first time within the Gaussian 09 program. It was applied to four test cases, docking to cytidine deaminase and human carbonic anhydrase II proteins. The docking results show the method's promise in resolving false-positive docking poses and improving the predicted binding modes over a conventional docking scheme. Finally, semiempirical QM methods which include dispersion and hydrogen-bond corrections were assessed for modelling conformations of β-cyclodextrin (βCD) and their adsorption on graphene. The closed in vacuo βCD cccw conformer was found to be in the lowest energy, in good agreement with previous ab initio QM studies. DFTB3, PM6-DH2 and PM7 methods were applied to model the intermolecular interactions of large βCD/graphene complexes, over a thousand atoms in size. We found that the binding preference of βCD on graphene is in a closed conformation via its C2C3 rim, agreeing with reported experimental and computational findings.