In biological systems, DNA formation occurs due to complementary H-bond interactions between nucleobases, as well as hydrophobic supramolecular interactions. It inspired polymer chemists in the development of supramolecular artificial platforms based on nucleobase-containing polymers. Despite their biomimetic nature and their huge potential to develop bioinspired supramolecular assemblies, nucleobase-containing polymers are in their infancy. The first part of this review aims to highlight the synthetic challenges related to the synthesis of nucleobase-containing monomers and polymers. The second part illustrates how to guide supramolecular interactions of nucleobase-containing copolymer architectures in order to obtain particular morphologies of the resulting supramolecular systems.