Synthetic chemists have developed
robust methods to synthesize
discrete molecules, linear and branched polymers, and disordered cross-linked
networks. However, two-dimensional polymers (2DPs) prepared from designed
monomers have been long missing from these capabilities, both as objects
of chemical synthesis and in nature. Recently, new polymerization
strategies and characterization methods have enabled the unambiguous
realization of covalently linked macromolecular sheets. Here we review
2DPs and 2D polymerization methods. Three predominant 2D polymerization
strategies have emerged to date, which produce 2DPs either as monolayers
or multilayer assemblies. We discuss the fundamental understanding
and scope of each of these approaches, including: the bond-forming
reactions used, the synthetic diversity of 2DPs prepared, their multilayer
stacking behaviors, nanoscale and mesoscale structures, and macroscale
morphologies. Additionally, we describe the analytical tools currently
available to characterize 2DPs in their various isolated forms. Finally,
we review emergent 2DP properties and the potential applications of
planar macromolecules. Throughout, we highlight achievements in 2D
polymerization and identify opportunities for continued study.