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 <i>ZT</i>; in some instances, <i>ZT</i> > 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-<i>m</i>, nanoscale mixtures of half-Heusler and Heusler compounds, ternary chalcogenide compounds of type <i>ABX<sub>2</sub></i> where the electronic structure near the band gap depends sensitively on the ordering of <i>A</i> and <i>B</i> atoms, and naturally occurring bulk superlattices formed out of alternating ionic and semiconducting bilayers as in SrFAgTe.
We have investigated the electronic structures of bulk GaSe and GaTe as well as the nature of defect states
associated with substitutional impurities and vacancies in GaSe and GaTe. These calculations were done using <i>ab initio</i>
density functional theory and supercell models. We find that the Ga-Ga dimers play an important role in the formation of
defect states. Analysis of the charge densities and the band structures associated with the defect states indicates that they
are strongly localized. Theoretical results are in good agreement with experiment for Cd<sub>Ga</sub> and V<sub>Ga</sub> in GaSe and for V<sub>Ga</sub>
in GaTe. The effect of spin-orbit interaction on the band structure of GaTe has been investigated; it is found that the top
valence bands at the Γ-point shift up in energy by ~ 0.1 eV due to the mixing of Te p<sub>x</sub>-p<sub>y</sub> and p<sub>z</sub> bands.