With the increasing cognition of the importance of organic molecules, they are widely applied in printing, biological and pharmacological fields, because of their special capabilities of harvesting solar light, scavenging free radicals, and chelating metal ions. During the past decades, the unique photoelectronic and photochemical properties of organic molecules, such as phthalocyanine, cyanidin, and their relevant derivatives, attract tremendous attention, because they provide an excellent opportunity to solve the worldwide energy crisis by converting directly the solar light to electricity. The surface morphology and electronic interaction of these organic molecules with other molecules, surfaces or interfaces play a critical role in determining the performance of the electronic and optical devices based on organic molecules. In this thesis, we focus on the investigation of several selected organic molecules, and their interaction with molecules, inorganic semiconductors, and organic semi-conductors, by using first-principles electronic structure calculations based on density functional theory, and time-dependent density functional theory. Particular attention is paid to the atomic structure, electronic and optical properties of organic molecules and the corresponding interfaces. The focus of this thesis is on the following aspects of the organic molecules: (i) The complexation mechanism of flavonoids with metal ions. The most likely chelation site for Fe is the 3-hydroxyl-4-carbonyl group, followed by 4-carbonyl-5-hydroxyl group and the 3'-4' hydroxyl (if present) of quercetin. A complex of two quercetin molecules with a single Fe ion is energetically more stable, however, six orbitals of Fe in the three quercetin complex are saturated by three perpendicular molecules to form and octahedral configurations. Furthermore, the optical absorbance spectra serves as signatures to identify various complexes. (ii) The electronic coupling between a dye molecule (Cyanidin) and a TiO2 nanowire. Upon molecular adsorption on TiO2 [010]-wire, cyanidin will be deprotonated into the quinonoidal form. This results in its highest occupied molecular orbitals being located in the middle of TiO2 bandgap and its lowest occupied molecular orbitals being close to the TiO2 conduction band minimum, in turn enhancing visible light absorption. Moreover, the excited electrons are injected into TiO2 conduction band within a time scale of 50 fs with negligible electron-hole recombination. (iii) The atomic and electronic structure of copper (fluoro-)phthalocyanine and graphene. When adsorbed on graphene, F16CuPc molecules prefer to form a close-packed hexagonal lattice with two-ordered alternating α and β stripes, whereas CuPc would like to form a square lattice. In addition, phthalocyanine adsorption modifies the electronic structure of graphene introducing intensity smoothing at 2-3 eV below and a small peak at ∼0.4 eV above the Dirac point in the density of states. And finally, (iv) the electronic interaction between CuPc and fullerene. For CuPc/C60 molecular complex, CuPc prefers to lie flat on the C60 surface rather than taking the standing-up molecular orientation. The favorable adsorption site for CuPc is the bridge site of C60 with one N-Cu-N bond of CuPc being parallel to a C-C bond of C60. Based on the analysis of the molecular complex, we predict that CuPc/C60(001) thin film heterojunction adopting the lying-down molecular orientation should have a higher efficiency of charge transfer in comparison with the relevant CuPc/C60(111) heterojunction with the standing-up arrangement.