The thermoelectric (TE) phenomenon involves direct conversion of thermal-to-electric energy, and is considered one of the smartest approaches to sustainable energy, by harnessing the waste thermal energy. Despites recent advances in improving the efficiency of TE materials over the last decades, new and better preforming TE materials are still sought after to meet future clean energy requirements. One major contribution to improve the efficiency of material is to reduce their lattice thermal conductivity. Three main factors are ascribed to lower thermal conductivity of a bulk material: (i) the presence of heavy elements in the structure, (ii) the relatively low symmetry and large unit cell, and (iii) the 'rattling' motion of the most electropositive atoms inside large cavities or channels. Quantifying the effect of complex bonding and chemical interactions on lattice thermal conductivity can be challenging. However, the role of the primitive unit cell volume is more clearly defined, as it dictates the number of phonon states within the first Brillouin zone, thus, providing short mean path lengths for the heat carrying phonons. Due to their peculiar structural chemistry that can result from the combination of ionic and covalent bonding, Zintl phases have emerged as promising candidates for superior TE properties. Particularly, the ternary pnictide Zintl phases as they usually exhibit intrinsic semiconducting properties with narrow energy band gap, and they feature complex polyanions and large channels or cages as their most common structural motives. The rigid anionic networks of covalent bounded atoms are suitable for the electron crystal part whereas the cationic substructure that consists of encapsulated rattling atoms is adequate for phonon-glass behavior, thereby complying with Slack's model of phonon-glass electron crystal (PGEC) materials. Consequently, high TE efficiencies were identified in ternary pnictides Zintl phases with heaviest alkaline-earth metals (A= Ca, Sr, Ba), or Eu and Yb. This large family of materials are characterized by enhanced complexity of their crystal structures and semiconducting behaviors. Notable examples are II-V and III-V ternary pnictides Zintl phases with group 12 and group 13 elements, respectively, that include Yb14MnSb11 (14-1-11 family), A5Tr2Pn6 family (Tr = Al, Ga, In) and 2-1-2 family A2CdPn2 (Pn = As, Sb, Bi). Surprisingly, Bi representatives of this class of pnictide TE materials are scarce when compared to lighter As and Sb phases, and only few binary bismuthides like A11Bi10, A16Bi11 and A2ZnBi2 phases have been investigated in relation with their thermoelectric properties. In fact, II-V and III-V ternary bismuthide Zintl phases are particularly warranted, because the substitution of Sb by heaviest Bi atoms is expected to result in lower lattice thermal conductivity and therefore, better TE efficiency. In addition, bismuth is the heaviest stable element in the Periodic Table of the elements, and the strength of the spin-orbit interaction increases with the atomic number. Since topological insulators exhibit band inversion driven by the spin-orbit interactions, bismuthide Zintl phases are expected to exhibit highest TE performance compared to lighter analogues. In fact, the most common and successful strategy to increase the efficiency of TE materials has been to modifying an already promising compound by introducing point defects mainly through alloying. The resulting isostructural solid solutions have much lower lattice thermal conductivity, due to the strong phonon scattering by the introduced point defects. This can result in a minimum of thermal conductivity at some composition, which is called the "alloy limit". Hence, nano-structuring of the much promising TE compounds have led to much better performing materials according to experimental results, mainly due to the phonon scattering at the grains boundaries. Having these findings in mind, one can surmise that complex multicomponent (or intergrowth) crystalline systems with semiconducting properties are of great interest for thermoelectric applications, since they consist of two or more building blocks, assembled in a manner that is reminiscent of nano-structuring, although on a smaller scale and in a periodic fashion. In addition, intergrowth structures also facilitate the tuning of their properties via specific chemical substitutions at different types of the chemically distinct building blocks. Consequently, in order to search for new material with enhanced structural complexity, we are exploring quaternary systems by blending the II-V and III-V bismuthide Zintl phases, with heaviest alkaline-earth (Ca, Sr, Ba) or divalent rare-earth (Eu, Yb) as active metals. These systems are expected to combine the crystal chemistry of the two closely related II-V and III-V classes of pnictide TE materials in single lattices and, due to differences in atomic sizes and valence states between group 12 and group 13 elements, a coordination site preference is anticipated in these quaternary (II/III)-V structures with huge impact expected on the structural complexity as well as the electronic band degeneracy. Noteworthy, ternary heteroatomic bismuthide anions, like the (II/IV)-V bismuthide cluster [Zn6Sn3Bi8] 4-, have been characterized in numerous Zintl salts with sequestered cations. However, corresponding quaternary bismuthide Zintl phases featuring ternary polyanionic systems are still missing.