Prescribed performance control (PPC) methodology, as a potential high-quality control method, has gained considerable attention due to its quantitative description for the transient and steady-state control performance in recent years. Thus, this chapter constructs a survey for the PPC methodology and aerospace application of PPC in the existing reported works. First, an overview on the origin, development, and characteristics of PPC method is presented. Then, the fundamental concepts about PPC are introduced and discussed, including the common types and properties of performance functions, ways to deal with the performance constraint that can achieve the prescribed performance. Finally, with introduction of some vital aerospace applications in the existing reported works, such as attitude control systems, multiple spacecraft systems and other flight vehicles, potential open issues of the PPC methodology are analyzed.