Pseudobinary phases (SnSe) BiSe exhibit a very diverse structural chemistry characterized by different building blocks, all of which are cutouts of the NaCl type. For SnSe contents between x = 5 and x = 0.5, several new phases were discovered. Next to, for example, SnBiSe ( x = 4) in the NaCl structure type and SnBiSe ( x = 0.5) in the layered defect GeSbTe structure type, there are at least four compounds (0.8 ≤ x ≤ 3) with lillianite-like structures built up from distorted NaCl-type slabs (L4,4-type SnBiSe, L4,5-type SnBiSe, L4,7-type SnBiSe, and L7,7-type SnBiSe). For two of them (L4,7 and L7,7), the cation distributions were determined by resonant X-ray scattering, which also confirmed the presence of significant amounts of cation vacancies. Thermoelectric figures of merit ZT range from 0.04 for SnBiSe to 0.2 for layered SnBiSe; this is similar to that of the related compounds SnBiTe or PbBiTe. Compounds of the lillianite series exhibit rather low thermal conductivities (∼0.75 W/mK for maximal ZT). More than other "sulfosalts", compounds in the pseudobinary system SnSe-BiSe adapt to changes in the cation-anion ratio by copying structure types of compounds containing lighter or heavier homologues of Sn, Bi, or Se and can incorporate significant amounts of vacancies. Thus, (SnSe) BiSe is a multipurpose model system with vast possibilities for substitutional and structural modification aiming at the optimization of thermoelectric or other properties.