This paper provides a survey of research activities of Large spaceborne deployable antennas (LSDAs) in the past, present and future. Firstly, three main kinds of spaceborne antennas, such as solid reflector, inflatable reflector and mesh reflector, are issued by showing the strengths and weaknesses. Secondly, a detailed research situation of LSDAs with mesh is discussed, for majority of the in-orbit large diameter and high frequency antennas are made in this type of structures. Thirdly, new conception of antenna is proposed as it does have both advantages of large aperture (high gain) and high precision (high frequency). Fourthly, the design theory and approach of LSDAs are concerned. It includes thermal-electromechanical multidisciplinary optimization, shaped beam design technique, performance testing technology and evaluation method, passive intermodulation of mesh, and application of new materials. Finally, the ultra large spaceborne deployable antennas of the next generation are presented, such as the deployable frame and inflatable reflector antennas, space-assembled ultra large antennas, smart array antennas and so on.