An airfoil is the geometric shape of a cross-section of a wing. When it is exposed to the flow of a fluid over its surface, it generates both lift and drag forces through a pressure distribution. Designing an efficient airfoil for aerodynamic applications is a complex challenge in the field of aerodynamic engineering, with the aim of achieving an optimal lift-to-drag ratio. The success of airfoil design hinges on the effective reduction of drag force under specific conditions, while simultaneously attaining the desired lift without encountering significant flow separation, such as boundary layer shedding. Furthermore, the design must adhere to lifting force limitations and meet structural requirements. In the field of airfoil design and optimization, literature review articles provide a valuable resource by offering an overview of the latest advancements in specific areas. These areas encompass a wide range of topics including the design and testing of adaptive geometry wings, such as morphing wing technology as well as the application of shape optimization techniques to enhance airfoil performance. Our goal is to provide researchers with an in-depth review of relevant articles published to date, examining the applied approaches utilized to tackle the complex problem of airfoil design and explore the methodology employed to address it, from a broad perspective on the topic.