A brief review of theoretical calculations of wavelengths and intensities of fluorescence and phosphorescence is presented. On the basis of theoretical calculations on transition energies, transition dipole moments, and spin-orbit couplings, our previous papers [J. Phys. Chem. A 110, 13295 (2006); J. Phys. Chem. C 111, 6897 (2007)] reported the reason why bis-[2-(2-thienyl) pyridine] platinum (Pt(thpy)(2)) and tris-(2-phenylpyridine) iridium (Ir(ppy)(3)) are electro-phosphorescent. Fast intersystem crossing to the lowest triplet, fast emission from the triplet, and slow non-radiative transition to the ground state should occur in effective phosphorescent molecules. In order to design new better materials for organic EL devices, non-radiative decay rates also need to be estimated in the series of our investigations. For the purpose of direct comparison between radiative and non-radiative transition rates, intra-molecular vibrational relaxation needs to be explicitly described. Since EL molecules are doped into host-molecule layers, the importance of the interaction between EL molecules and host molecules is discussed. Tentative results of quantum-mechanics/molecular mechanics (QM/MM) calculations are presented for the luminescent layer.