The preparation of polythioethers has gained importance again after the development of click chemistry reactions. The thiol-X reactions, i.e., thiol-ene reactions based on free radical mechanism facilitated by light or heat, and thiol-Michael and thiol-epoxy reactions, which are the main synthetic pathways for the synthesis of polymers (linear, hyperbranched (HB), and network) with thioether linkages and meet most of the features of click reactions strategy, have currently been revisited. For a while, our group has focused on synthesizing linear, HB, and network polythioethers based on electron-deficient alkyne-containing precursors. We have shown that electron-deficient alkyne-containing monomers and polymers offer a suitable platform for thiol-Michael (i.e., thiol-yne) click reactions to yield linear, HB, and network structures rapidly under ambient conditions. The central structure in these polythioether syntheses is electron-deficient alkyne bonds of acetylenedicarboxylates, which are then reacted with dithiols in chloroform through an organobase 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) at ambient temperatures. Moreover, acetylenedicarboxylates are functionalized using copper-free azide-alkyne cycloaddition reaction followed by reacting with multifunctional allyl and SH derivatives through thiol-ene photopolymerization resulting in polymeric networks with thioether linkages. This feature article highlights our contribution to the synthesis of linear, HB, and network polythioether based on various electron-deficient alkyne precursors.