The self-assembly of particles into organized structures is ubiquitous in nature. In this talk I will discuss two examples of self-assembly. The first involves the case of man-made Janus particles, named after the two-faced Greek god because such particles have one face which is hydrophobic and the other hydrophilic, say. Janus particles will avoid one another if they face one way but gather together if they face the other direction. This combination of incompatible elements in the same basic unit structure causes such particles to assemble spontaneously into complex superstructures, such as micelles, vesicles, chains or lattices. Natural examples of Janus particles are phospholipids, which are a key element in cell membranes. We discuss here recent work by our group on Janus ellipsoids, including the possibility that micelles made of ellipsoids can provide a mechanism for drug delivery. The second case I will discuss is a study of the self-assembly of amelogenin protein molecules, which play a fundamental role in the development of dental enamel. This is just one example of biomineralization in nature.