In light of the considerable impact synthetic 2D polymers are expected to have on many fundamental and applied aspects of the natural and engineering sciences, it is surprising that little research has been carried out on these intriguing macromolecules. Although numerous approaches have been reported over the last several decades, the synthesis of a one monomer unit thick, covalently bonded molecular sheet with a long-range ordered (periodic) internal structure has yet to be achieved. This Review provides an overview of these approaches and an analysis of how to synthesize 2D polymers. This analysis compares polymerizations in (initially) a homogeneous phase with those at interfaces and considers structural aspects of monomers as well as possibly preferred connection modes. It also addresses issues such as shrinkage as well as domain and crack formation, and briefly touches upon how the chances for a successful structural analysis of the final product can possibly be increased.