Dynamic covalent polymers are materials formed by reversible covalent bonds and non-covalent interactions through an adaptive constitutional dynamic chemistry. The implementation of dynamic covalent polymers in gene delivery has recently emerged due to their responsive and adaptive features. Indeed, such an approach offers the alluring promise of discovering optimal delivery vectors self-fitted to their nucleic acid cargos and responsive to environmental changes (e.g. pH changes or the presence of a biomolecular target). This review will discuss more precisely the structural features of the molecular building blocks used so far, the architecture of the resulting dynamic covalent polymers from linear to 2D and 3D, and the covalent and supramolecular self-assembly processes at play in nucleic acid recognition and delivery, showcasing in particular the very few examples of adaptive self-assembly of dynamic covalent polymers templated by nucleic acids and responsive to the presence of biomolecular targets found in cell membranes that facilitate cell entry.