This paper describes the outcomes of a study funded by the European Space Agency aimed at identifying the technical challenges and trade-offs at the system level, performing preliminary designs of an active correction loop for large deployable telescopes, and defining technological roadmaps for the development of the active correction loop for the selected designs.This study has targeted two very different application cases, one for High Resolution Earth Observation from Geostationary orbit (called GeoHR, with a 4m diameter entrance pupil) and one for Science missions requiring very large telescopes (with a up to 18 m diameter entrance pupil) with high-contrast imaging capabilities for exo-Earth observations and characterization.For both application cases, this paper first summarizes the mission objectives and constraints that have influence on the telescope designs. It then presents the high-level trade-offs that have been led and the optical and mechanical design that have been developed, including the deployable aspects.Finally, the performance assessment is presented, and is the basis for the justification of an active optics correction chain, with a preliminary set of requirements for typical components of the system. The presentation is concluded with proposed technological roadmaps that aim to allow the development of the building blocks on which the next generation instruments will be able to rely on.