Supramolecular polymers are assembled from monomeric units held together by reversible non-covalent interactions. These supramolecular materials display polymeric properties and may soon have important industrial applications. This mini review focuses on the advances in main-chain supramolecular polymers whose assembly is guided primarily by hydrogen bonding interactions. The design constraints of these new systems discussed include assembly motifs, the strength and directionality of the non-covalent interactions, association versus reversibility, and environmental effects on the degree of polymerization. Selected literature examples including Meijer's ureidopyrimidinone system are used to highlight the challenges and potential of these supramolecular polymeric materials.