With the rapid development of scanning probe microscopy, it has become possible to study polymerization processes on suitable surfaces at the atomic level and in real space. In the two-dimensional confinement of a surface, polymerization reactions can give rise to the formation of unprecedented polymers with unique structures and properties, not accessible in solution. After a little over one decade since the discovery of covalent on-surface polymerization, we give an overview of the field, analyse the crucial aspects and critically reflect on the status quo. Specifically, we provide some general considerations about fundamental mechanisms as well as kinetics and thermodynamics of on-surface polymerization processes. The important role of the surface is detailed in view of its ability to control polymer formation with regard to structure, dimensionality and composition. Furthermore, examples that allow for locally induced polymerization are highlighted. Finally, we provide an analysis of scientific challenges in the field and outline future prospects.
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