Two-dimensional (2D) polymers have garnered widespread interest because of their intriguing physicochemical properties. Envisaged applications in fields including nanodevices, solid-state chemistry, physical organic chemistry, and condensed matter physics, however, demand high-quality and large-scale production. In this perspective, we first introduce exotic band structures of organic frameworks holding honeycomb, kagome, and Lieb lattices. We further discuss how mesoscale ordered 2D polymers can be synthesized by means of choosing suitable monomers and optimizing growth conditions. We describe successful polymerization strategies to introducing a non-benzenoid subunit into a π-conjugated carbon lattice via delicately designed monomer precursors. Also, to obviate transfer and restore the intrinsic properties of π-conjugated polymers, new paradigms of aryl-aryl coupling on inert surfaces are discussed. Recent achievements in the photopolymerization demonstrate the need for monomer design. We conclude the potential applications of these organic networks and project the future possibilities in providing new insights into on-surface polymerization.