The properties of 2D materials, such as graphene, arise not only from their composition but also their sheet-like structures. Synthetic 2D polymers made from well-defined monomers promise to expand the range of such materials, but are very difficult to synthesize. A collection of articles in this Focus highlights some of the latest research in making and characterizing single-crystal synthetic 2D polymers, and also considers the challenges and potential for these materials in the future.