Numerous supramolecular platforms inspired by natural self-assembly are exploited as drug delivery systems. The spontaneous arrangement of single building blocks into inorganic and organic structures is determined and controlled by noncovalent forces such as electrostatic interactions, π-π interactions, hydrogen bonds, and van der Waals interactions. This review describes the main structures and characteristics of several building blocks used to obtain stable, self-assembling nanostructures tailored for numerous biological applications. Owing to their versatility, biocompatibility, and controllability, these nanostructures find application in diverse fields ranging from drug/gene delivery, theranostics, tissue engineering, and nanoelectronics. Herein, we described the different approaches used to design and functionalize these nanomaterials to obtain selective drug delivery in a specific disease. In particular, the review highlights the efficiency of these supramolecular structures in applications related to infectious diseases and cancer.