Although an old reaction, the interest in the thiol-epoxy reaction, especially as a polymerization process, is only recent. The power of this chemistry lies in its efficiency and operation under ambient conditions, the commercial availability of a vast variety of thiol- and epoxide-carrying molecules that can be utilized as monomers, the long list of polymerization catalysts and associated solvent systems, and the formation of a hydroxyl group upon completion. The amine-epoxy reaction bears similar hallmarks, but is relatively simpler as a catalyst is not required for this process. Moreover, in comparison with the thiol-epoxy system, which may sometimes give rise to disulfide defects through oxidative dimerization of thiols, the amine-epoxy system is comparatively more robust and insensitive to such a side reaction. The polymers resulting from thiol-epoxy and amine-epoxy reactions are termed as poly(β-hydroxythio-ether)s and poly(β-hydroxyl amine)s, respectively. The polymerization process itself is referred to as 'proton transfer polymerization'. This is because quenching of the alkoxide anion, generated upon the nucleophilic attack of the thiolate or amine moiety on the epoxide unit, through protonation, is the critical step that ultimately decides the nature of propagation and the final structure of the polymer. It is understood that multiple proton donors can exist within a polymerization system. Our attempt here is to document the growing interest in the aforementioned chemistries as a polymerization process. Since the backbones are reactive, we will also detail post-polymerization modification approaches of these polymers. Last but not least, an overview is given and the future directions are identified.