The invariant appearance of the mu8 coordination mode for the C4(2-) dianion in its silver(I) complexes, with four silver(I) atoms attached to each terminal ethynide moiety, implies that the Ag4[cap]C[triple bond]C-C[triple bond]C[cap]Ag4 species may be considered as a new type of supramolecular synthon for the construction of 1D, 2D, and 3D coordination polymers. This Focus Review covers recent results on the synthesis and structural characterization of silver(I) arylethynide and alkylethynide complexes, which established the existence and utility of analogous polynuclear supramolecular synthons R-C[triple bond]C[cap]Ag(n) (R = aryl or alkyl; n = 4, 5) and Ag(n)[cap]C2-R-C2[cap]Ag(n) (R = p-, m-, o-C6H4; n = 4, 5). The interplay of silver-ethynide bonding, which can be classified into sigma, pi, and mixed (sigma,pi) types, with argentophilicity, pi-pi stacking, and other weak interactions highlights the complexity and challenge in building coordination networks of silver ethynide complexes.