Flexible antennas are widely used in mobile communications, the Internet of Things, personalized medicine, aerospace, and military technologies due to their superior performance in terms of adaptability, impact resistance, high degree of freedom, miniaturization of structures, and cost-effectiveness. With excellent flexibility and portability, these antennas are now being integrated into paper, textiles, and even the human body to withstand the various mechanical stresses of daily life without compromising their performance. The purpose of this paper is to provide a comprehensive overview of the basic principles and current development of flexible antennas, systematically analyze the key performance factors of flexible antennas, such as structure, process, material, and application environment, and then discuss in detail the design structure, material selection, preparation process, and corresponding experimental validation of flexible antennas. Flexible antenna design in mobile communication, wearable devices, biomedical technology, and other fields in recent years has been emphasized. Finally, the development status of flexible antenna technology is summarized, and its future development trend and research direction are proposed.