Dye-sensitized solar cells (DSCs) represent a promising approach to the direct conversion of sunlight to electrical energy at low cost and high efficiency. DSCs are based on a film of anatase TiO₂ nanoparticles covered by adsorbed molecular dyes and immersed in a liquid redox electrolyte. Upon photoexcitation of the chemisorbed dye, electrons are injected into the TiO₂ conduction band and can travel across the nanostructured film to reach the counter-electrode, while the oxidized dye is regenerated by the redox electrolyte. In this review we present a summary of recent computational studies of the electronic and optical properties of dye-sensitized TiO2 interfaces, with the aim of providing the basic understanding of the operation principles of DSCs and establishing the conceptual basis for their design and optimization.We start with a discussion of isolated dyes in solution, focusing on the dye's atomic structure, ground and excited state oxidation potentials, and optical absorption spectra. We examine both Ru(II)-polypyridyl complexes and organic "push-pull" dyes with a D-π-A structure, where the donor group (D) is an electron-rich unit, linked through a conjugated linker (π) to the electron-acceptor group (A). We show that a properly calibrated computational approach based on Density Functional Theory (DFT) combined with Time Dependent DFT (TD-DFT) can provide a good description of both the absorption spectra and ground and excited state oxidation potential values of the Ru(II) complexes. On the other hand, organic push-pull dyes are not well described by the standard DFT/TD-DFT approach. For these dyes, an excellent description of the electronic structure in gas phase can be obtained by the many body perturbation theory GW method, which has, however, a much higher computational cost.We next consider interacting dye/semiconductor systems. Key properties are the dye adsorption structure onto the semiconductor, the nature and localization of the dye@semiconductor excited states, and the alignment of ground and excited state energy levels at the dye/semiconductor heterointerface. These properties, along with an estimate of the electronic coupling, constitute the fundamental parameters that determine the electron injection and dye regeneration processes. For metallorganic dyes, standard DFT/TDDFT methods are again found to reproduce accurately most of the relevant electronic and optical properties. For highly conjugated organic dyes, characterized by a high degree of charge transfer excited states, instead, the problems associated to the charge-transfer nature of their excited states extend to their interaction with TiO₂ and translate into an erroneous description of the relative energetics of dye/semiconductor excited states. A full description of push-pull organic dyes/semiconductor excited states, which is essential for modeling the key process of electron injection in DSCs, still represents a challenge which should be addressed by next generation DFT or post-DFT methods.