Thanks to the recent development in diffractive optical element (DOE) fabrication technique, large aperture diffractive telescope systems have been tremendously studied to achieve high-resolution imaging. In this review, the universal optical design mechanism of a diffractive telescope system is initially elucidated, and the state-of-art progresses of large aperture diffractive optical telescopes are overviewed. Then, we analyze DOE lithography technique, from which we can fabricate DOEs on different substrates. Moreover, we also present subaperture stitching, so that we can obtain large aperture DOEs. Afterwards, different experimentally implemented ground-based diffractive telescope systems are reviewed by emphasizing their advantages. Finally, we propose the prospects with respect to the arising challenges in large aperture diffractive telescope systems. © 2020 Elsevier Ltd