Thermoelectric materials are of great current interest for a number of energy-related applications such as waste heat recovery, terrestrial cooling, and thermoelectric power generation. There have been several significant recent advances in improving the thermoelectric figure of merit ZT; in some instances, ZT > 2 at high temperatures. Concepts like electron-crystal phonon-glass, dimensional confinement, nanostructuring, energy filtering, and intrinsic lattice anharmonicity have not only acted as guiding principles in synthesizing new materials but also for electronic structure engineering using theoretical calculations. In this review paper, we discuss these concepts and present a few examples of theoretical studies of electronic structure and transport properties illustrating how some of these ideas work. The four types of systems we discuss are quaternary chalcogenides LAST-m, nanoscale mixtures of half-Heusler and Heusler compounds, ternary chalcogenide compounds of type ABX2 where the electronic structure near the band gap depends sensitively on the ordering of A and B atoms, and naturally occurring bulk superlattices formed out of alternating ionic and semiconducting bilayers as in SrFAgTe.