Research in thermoelectric (TE) quantum structures was greatly propelled by the prediction in the early 1990s of a significant boost in TE efficiency by quantum size effects. Recently, research interest has shifted from quantum size effects in conventional semiconductors toward new types of quantum materials (e.g., topological insulators [TIs], Weyl and Dirac semimetals) characterized by their nontrivial electronic topology. Bi2Te3, Sb2Te3, and Bi2Se3, established TE materials, are also TIs exhibiting a bulk bandgap and highly conductive and robust gapless surface states. The signature of the nontrivial electronic band structure on TE transport properties can be best verified in transport experiments using nanowires and thin films. However, even in nanograined bulk, the typical peculiarities in the transport properties of TIs can be seen. Finally, the remarkable transport properties of Dirac and Weyl semimetals are discussed.