Abstract: Curved conformal antennas significantly enhance radar detection range and system performance while ensuring the host platform maintains excellent aerodynamic characteristics and stealth capabilities, and become a key focus area for the development of new-generation radar systems. In this paper, based on the morphology of conformal antennas, curved conformal antennas are categorized into four major types: planar-fitted antenna, passive conformal antenna, flexible conformal antenna, and integrated active conformal antenna. Firstly, a comprehensive review of the research status of conformal antennas of various morphologies is provided, summarizing the gaps in the development of conformal antenna technology between domestic and international efforts. Then, the progress in key common technologies for curved conformal antennas, including overall design, electromechanical-thermal coupling technology, conformal modeling technology, and integrated manufacturing of curved surface circuits, has been explored in this paper. Finally, an outlook on the future development trends of curved conformal antennas is provided in this paper.