The membrane antenna technology is a very promising approach to obtain large aperture with light weight and low stowed volume. In the past decades, extensive studies have been carried out on active and passive membrane antennas. However, the practical spaceborne applications are rare due to many challenges, e.g., the surface accuracy maintenance, the on-orbit reliability, and the environmental compatibility. This paper summarizes the history and state-of-art progresses on spaceborne membrane antennas. Curved surface reflectors, conformal active membrane antennas, planar array membrane antennas, and planar reflectarray membrane antennas have been introduced, respectively. Radiofrequency design, deploying mechanism, material, experiment, application, and analysis method have been presented. By concluding the advantages and challenges of the current membrane antennas, this paper is aimed at providing a perspective of the existing problems and future trend of spaceborne membrane antennas.