The development of four kinds of parabolic antenna structures is presented, including radial rib antenna structure, wrapped rib antenna structure, truss antenna structure and hoop antenna structure. A detailed comparison of these four structures is presented. Additionally, for the planar antenna structures, the features of wing antenna structures, truss antenna structures and membrane antenna structures are summarized. Finally, future trends of large, high packing factor and high surface accuracy are pointed out. And the technical difficulties which should be overcome before space applications of larger and higher precision SAR antennas are proposed.