Self-assembly has been recognised as a ubiquitous aspect of modern chemistry. Our understanding and applications of self-assembly are substantially based on what has been learned from biochemical systems. In this review, we describe various aspects of self-assembly commencing with an account of the soft structures that are available by assembly of surfactant amphiphiles, which are important scientific and industrial materials. Variation of molecular design using rules defined by surfactant self-assembly permits synthesis of functional nanostructures in solution and at surfaces while increasing the strength of intermolecular interactions through π-π stacking, metal cation coordination and/or hydrogen bonding leads to formation of highly complex bespoke nanostructured materials exemplified by DNA assemblies. We describe the origins of self-assembly involving aggregation of lipid amphiphiles and how this subject has been expanded to include other highly advanced chemical systems.