A full understanding of the elementary processes taking place in dye-sensitised solar cells requires an accurate description of the electronic structure of the dyes, the semiconductor surface, the electrolyte and their interactions. This review describes how electronic structure calculations have contributed to the field since its first steps and what methodologies have been adopted to study the charge transfer processes at the interface. Not all properties are equally predictable with electronic structure methods, and this work highlights the main success areas (e.g. the rationalization of the optical properties of the dyes), the recent developments (e.g. the improved description of the dye–semiconductor interaction) and the key challenges for the future (e.g. the calculation of charge recombination rate).