Abstract: A deployable space telescope with an aperture bellow one meter can be realized easily by using foldable multipod parallel structures based on tape springs to support the secondary mirror of a Cassegraintype telescope and by adjusting the structures on orbit. This paper introduces the structural features of the deployable space telescopes based on tape springs, and presents the research advances in the four techniques published in recent years for the space telescope precision deployments based on tape springs, namely, quadripod, octapod, tripod, and hexapod supports. It suggests that research on the precision deployments of space telescopes based on tape springs in future should put the focuses on the modelling and optimizing of deployment structures and the measurement and correction of the deployment deviation. Moreover, making an experiment in simulated gravity environments will be conductive to better research on the structure dynamics and deployment precision. Also, the development of an asymmetric deployable structure is a good choice for an offaxis telescope. Finally, it indicates that the improvement of deployment structures for space telescopes reported here will be a promising technique for highresolution remote sensing imaging and free space optical communications.