Coinage-metal(I) polychalcogenide halides represent a new class of materials featuring high ion dynamics of different substructures capable of an effective phonon scattering process in the solid state. The interplay of mobile coinagemetal ions such as Ag + or Cu + on the one hand and the temperature-driven redox reaction of a linear, partially covalent-bonded Te chain on the other hand is responsible for tremendous variations in the electronic structure of such materials. A huge drop of the Seebeck coefficient within a very small temperature range and an extremely low thermal conductivity are the key properties of Ag 10 Te 4 Br 3 , the first representative of this substance class. Two different sets of compounds with the general formula (CM) 10 Q 4 X 3 and (CM) 23 Q 12 X (CM = coinage metal Cu or Ag, Q = chalcogen, X = halogen) have been found, and recent experiments point toward the existence of formerly unknown copper(I) (poly)chalcogenide halides and two more silver(I) (poly)chalcogenide halides in this field. A comparable linear Te chain is present in a number of different compounds such as some alkaline-earth polychalcogenides M 5 Te 3 , the mineral stuetzite Ag 4.5 Te 3 , and the closely related compounds Ag 11 AsTe 7 and Ag 12 Te 6 S. In most cases the thermoelectric potential of these materials has not been verified. A topological approach for the description of the structural features has been developed to understand the electronic properties of these complex materials in detail.