In this paper, we survey recent advances in the self-assembly processes of novel functional platforms for nanomaterials and biomaterials applications. We provide an organized overview, by analyzing the main factors that influence the formation of organic nanostructured systems, while putting into evidence the main challenges, limitations and emerging approaches in the various fields of nanotechology and biotechnology. We outline how the building blocks properties, the mutual and cooperative interactions, as well as the initial spatial configuration (and environment conditions) play a fundamental role in the construction of efficient nanostructured materials with desired functional properties. The insertion of functional endgroups (such as polymers, peptides or DNA) within the nanostructured units has enormously increased the complexity of morphologies and functions that can be designed in the fabrication of bio-inspired materials capable of mimicking biological activity. However, unwanted or uncontrollable effects originating from unexpected thermodynamic perturbations or complex cooperative interactions interfere at the molecular level with the designed assembly process. Correction and harmonization of unwanted processes is one of the major challenges of the next decades and requires a deeper knowledge and understanding of the key factors that drive the formation of nanomaterials. Self-assembly of nanomaterials still remains a central topic of current research located at the interface between material science and engineering, biotechnology and nanomedicine, and it will continue to stimulate the renewed interest of biologist, physicists and materials engineers by combining the principles of molecular self-assembly with the concept of supramolecular chemistry.