How do animals acquire their various skin patterns? Although this question may seem easy, in fact it is very difficult to answer. The problem is that most animals have no related structures under the skin; therefore, the skin cells must form the patterns without the support of a prepattern. Recent progress in developmental biology has identified various molecular mechanisms that function in setting the positional information needed for the correct formation of body structure. None of these can explain how skin pattern is formed, however, because all such molecular mechanisms depend on the existing structure of the embryo. Although little is known about the underlying molecular mechanism, many theoretical studies suggest that the skin patterns of animals form through a reactionβdiffusion systemβa putative βwaveβ of chemical reactions that can generate periodic patterns in the field. This idea had remained unaccepted for a long time, but recent findings on the skin patterns of fish have proved that such waves do exist in the animal body. In this review, we explain briefly the principles of the reactionβdiffusion mechanism and summarize the recent progress made in this area.