Extensive research has been made for nonlinear systems up to now, and significant results have been obtained. However, among the results, only special class of nonlinear systems are investigated, where system input powers are equal to one. The nonlinear systems with higher powers, especially their fault detection, fault estimation, and fault-tolerant control have not been thoroughly studied, which are the topics in this book. In this chapter, the survey of the systems with higher powers including known and unknown powers, their fault detection, fault estimation, and fault-tolerant control are introduced, and some problems studied in this book are formulated. Meanwhile, the main content of each chapter and the relationship between chapters also have been introduced.