Nucleobase-containing molecules are compounds essential in biology due to the fundamental role of nucleic acids and, in particular, G-quadruplex DNA and RNA in life. Moreover, some molecules different from nucleic acids isolated from different vegetal sources or microorganisms show nucleobase moieties in their structure. Nucleoamino acids and peptidyl nucleosides belong to this molecular class. Closely related to the above, nucleopeptides, also known as nucleobase-bearing peptides, are chimeric derivatives of synthetic origin and more rarely isolated from plants. Herein, the self-assembly properties of a vast number of structures, belonging to the nucleic acid and nucleoamino acid/nucleopeptide family, are explored in light of the recent scientific literature. Moreover, several technologically relevant properties, such as the hydrogelation ability of some of the nucleobase-containing derivatives, are reviewed in order to make way for future experimental investigations of newly devised nucleobase-driven hydrogels. Nucleobase-containing molecules, such as mononucleosides, DNA, RNA, quadruplex (G4)-forming oligonucleotides, and nucleopeptides are paramount in gel and hydrogel formation owing to their distinctive molecular attributes and ability to self-assemble in biomolecular nanosystems with the most diverse applications in different fields of biomedicine and nanotechnology. In fact, these molecules and their gels present numerous advantages, underscoring their significance and applicability in both material science and biomedicine. Their versatility, capability for molecular recognition, responsiveness to stimuli, biocompatibility, and biodegradability collectively contribute to their prominence in modern nanotechnology and biomedicine. In this review, we emphasize the critical role of nucleobase-containing molecules of different nature in pioneering novel materials with multifaceted applications, highlighting their potential in therapy, diagnostics, and new nanomaterials fabrication as required for addressing numerous current biomedical and nanotechnological challenges.