Computer Aided Geometric Design (CAGD) is a field of science that grows with the wind of technology behind it, developing day by day and enchanting us. It is an undeniable fact that the development process of this hot topic is based on mathematical foundations. At the core of this mathematical foundation lies the theory of Bézier curves. We conducted a study aiming to present the birth of Bézier curves, their historical development and especially their applications in the field of computer-aided geometric design with a rich spectrum. Another emerging field that we would like to draw your attention to here is reverse engineering. Discovering the function, structure and working principle of an object or system with an inferential reasoning method is included in the field of reverse engineering. At this point, it would be logical to say that the concepts of CAGD and reverse engineering support each other. We foresee that future researchers will contribute to the development and application process of Bézier curves, which are very useful in Computer Aided Design (CAD), CAGD and engineering, with different artificial intelligence-based algorithms and new tools. We see CAGD and other related fields as very bright and fruitful interdisciplinary fields that will culminate mathematician-engineer collaboration. This chapter presents a systematic review work referring to practice of Bézier curves theory and its solutions to the real-life problems in CAGD.