Coumarin-based dyes have been successfully used in dye-sensitized solar cells, leading to photovoltaic conversion efficiencies of up to about 8%. Given the need to better understand the behavior of the dye adsorbed on the TiO₂ nanoparticle, we report results of density functional theory (DFT) and time-dependent DFT (TD-DFT) studies of several coumarin-based dyes, as well as complex systems consisting of the dye bound to a TiO₂ cluster. We provide the electronic structure and simulated UV-Vis spectra of the dyes alone and adsorbed to the cluster and discuss the matching with the solar spectrum. We display the energy level diagrams and the electron density of the key molecular orbitals and analyze the electron transfer from the dye to the oxide. Finally, we compare our theoretical results with the experimental data available and discuss the key issues that influence the device performance.