Two-dimensional polymers (2DPs) are molecularly thin networks consisting of monomers covalently linked in at least two directions in the molecular plane. Because of the unique structural features and emergent physicochemical properties, 2DPs promise application potentials in catalysis, chemical sensing, and organic electronic devices. On-surface synthesis is of great interest to fabricate 2DPs with atomic precision, and the properties of the 2DPs can be characterized in situ through scanning probe techniques. In this Perspective, we first introduce the recent developments of on-surface 2D polymerization, including the design principle, the synthetic reactions, and the factors affecting the synthesis of 2DPs on surface. Then, we summarize some major challenges in this field, including the fabrication of high-quality 2DPs and the study of the intrinsic electronic properties of 2DPs, and we discuss some of the available solutions to address these issues.