The chemistry of N-heterocyclic carbenes (NHCs) has witnessed tremendous development in the past two decades: NHCs have not only become versatile ligands for transition metals, but have also emerged as powerful organic catalysts in molecular chemistry and, more recently, in metal-free polymer synthesis. To understand the success of NHCs, this review first presents the electronic properties of NHCs, their main synthetic methods, their handling, and their reactivity. Their ability to activate key functional groups (e.g. aldehydes, esters, heterocycles, silyl ketene acetals, alcohols) is then discussed in the context of molecular chemistry. Focus has been placed on the activation of substrates finding analogies with monomers (e.g. bis-aldehydes, multi-isocyanates, cyclic esters, epoxides, N-carboxyanhydrides, etc.) and/or initiators (e.g. hydroxy- or trimethylsilyl-containing reagents) employed in such "organopolymerisation" reactions utilizing NHCs. A variety of metal-free polymers, including aliphatic polyesters and polyethers, poly(alpha-peptoid)s, poly(meth)acrylates, polyurethanes, or polysiloxanes can be obtained in this way. The last section covers the use of NHCs as structural components of the polymer chain. Indeed, NHC-based photoinitiators, chain transfer agents or functionalizing agents, as well as bifunctional NHC monomer substrates, can also serve for metal-free polymer synthesis.