Membrane diffractive optical elements formed by fabricating microstructures on the substrates have two important characteristics, ultra-light mass (surface mass density < 0.1 kg/m2) and loose surface shape tolerances (surface accuracy requirements are on the order of magnitude of centimeter). Large-aperture telescopes using a membrane diffractive optical element as the primary lens have super large aperture, light weight, and low cost at launch. In this paper, the research and development on space-based diffractive telescopes are classified and summarized. First, the imaging theory and the configuration of diffractive-optics telescopes are discussed. Then, the developments in diffractive telescopes are introduced. Finally, the development prospects for this technology used as a high-resolution space reconnaissance system in the future are summarized, and the critical and relevant work that China should carry out is put forward.