The special and intrinsic characteristic of the compositional data is that the proportions of a composition are naturally subject to a unit-sum constraint. As a result, commonly used statistics cannot be directly applied. Aitchison (1986) introduced a set of methods on how to analyze the composition data appropriately, including partial least square analysis and Ternary diagrams. Using these methods, some successful applications have been reported in other fields, such as chemistry and geology. This presentation addresses the major problems and consequences by analyzing the composition data using inappropriate "standard" statistical methods. By reviewing a brief history of the development of new composition data analyses, the major existing methods will be described, including their statistical and mathematical principles, analytical steps, and related computer programs. Key issues in a composition data analysis will also be addressed, such as "How can the pattern of the integrative variability of compositional data be satisfactorily described?" and "How can the composition data analysis be conducted?" An empirical example data of the physical activity preferences in middle schools will be illustrated along with this presentation. Finally, limitations of the existing methods, as well as the future research directions, will be described.