The high visibility of fuzzy logic and mathematics based on fuzzy logic is primarily due to their highly successful applications in many areas of human affairs. The aim of this chapter is to characterize the evolution and current status of these applications. Covered are applications in the various areas of engineering, natural, social and earth sciences, psychology, medicine, management and business, decision making, pattern recognition, image analysis, risk analysis, music, among others. In each of these areas, the significance of using fuzzy logic and the associated mathematics is critically assessed. It is argued that in some application areas, such as psychology or quantum mechanics, a cooperation between researchers in fuzzy logic and those in the application domain, leading possibly to new types of nonstandard fuzzy sets, is essential for further progress.