A large variety of different interactions between the chalcogen atoms, Q, occur in the solid state structures of polyselenides and polytellurides, including both molecular and infinite units. The simplest motifs are classical Q(2)(2-) dumbbells and nonlinear Q(n)(2-) chains (n = 3, 4, 5, ..), e.g. found in alkali metal polychalcogenides. In addition, nonclassical so-called hypervalent motifs exist in the form of linear Q(3)(4-) units or within larger units such as Q(4)(4-) and Q(5)(4-). Infinitely extended Q units include zigzag, cis/trans and linear chains, as well as planar and slightly puckered layers. Several of those are susceptible to Peierls distortions, leading to the formation of both commensurate and incommensurate superstructures and anomalies in transport properties, including metal-nonmetal transitions.