This paper focuses on the syntheses, structures, and luminescence properties of 1D, 2D, and 3D coordination polymers built upon the tetranuclear Cu4X4 clusters and mono- and dithioether assembling ligands. A review of the relevant literature is presented along with our own results stressing on the salient features of the interactions between the CuI salt as the starting material and the thioethers. Among the features, the solvato- (lost or gain of a monothioether or solvent molecule) and luminescence thermochromism (temperature dependence of the emission) of the solids, and the enhanced versatility of the CuI salt to form clusters of different nuclearity (Cu2I2, Cu4I4, Cu6I6) and structures (closed cubane, partially open "flower-basket-like" cubane, and open cubane) upon the reaction conditions and ligands, are described. The steady state and time-resolved solid-state emission and excitation spectra (at 298 and 77 K) as well as the emission lifetimes are examined. Simple and apparently "innocent" modification may have a drastic effect on the polymer network and cluster structures, but this paper finds no obvious trend for the moment except for the ligand rigidity. The rhombic Cu2I2 and closed-cubane Cu4I4 clusters are the most encountered motifs whereas the open-flower-basket Cu4I4 cubane and the hexagonal Cu6I6 clusters are scarce.