To predict the fundamental properties of thermoelectric materials without anyadjustable parameters is now starting to get within reach. Knowledge about the electronic structure can give access to essential transport properties with predictive power, and many results may be compared directly to experiments at realistic conditions. A remaining challenge is to describe scattering of electrons and phonons in a realistic and quantitatively satisfactory manner. We describe efforts to describe transport phenomena and other properties in a selection of materials and systems. Examples include the Zn-Sb system, half-Heusler alloys, and Na- and Ca-cobalt oxides.