In recent years, structural colors have attracted great attention in a wide variety of research fields. This is because they are originated from complex interaction between light and sophisticated nanostructures generated in the natural world. In addition, their inherent regular structures are one of the most conspicuous examples of non-equilibrium order formation. Structural colors are deeply connected with recent rapidly growing fields of photonics and have been extensively studied to clarify their peculiar optical phenomena. Their mechanisms are, in principle, of a purely physical origin, which differs considerably from the ordinary coloration mechanisms such as in pigments, dyes and metals, where the colors are produced by virtue of the energy consumption of light. It is generally recognized that structural colors are mainly based on several elementary optical processes including thin-layer interference, diffraction grating, light scattering, photonic crystals and so on. However, in nature, these processes are somehow mixed together to produce complex optical phenomena. In many cases, they are combined with the irregularity of the structure to produce the diffusive nature of the reflected light, while in some cases they are accompanied by large-scale structures to generate the macroscopic effect on the coloration. Further, it is well known that structural colors cooperate with pigmentary colors to enhance or to reduce the brilliancy and to produce special effects. Thus, structure-based optical phenomena in nature appear to be quite multi-functional, the variety of which is far beyond our understanding. In this article, we overview these phenomena appearing particularly in the diversity of the animal world, to shed light on this rapidly developing research field.