Mechanisms of animal skin pigment pattern formation have long been of interest to developmental and mathematical biologists. Although there has been a well-studied theoretical hypothesis-the reaction-diffusion system-that is able to reproduce the variety of skin patterns, a lack of molecular evidence has kept it just a hypothesis. In this review, we summarize the results of theoretical studies to date for researchers not familiar with their mathematical underpinnings, and we discuss future approaches that will more fully integrate mathematical models and experimental analyses.