The space environment is regularly used for experiments addressing astrobiology research goals. The specific conditions prevailing in Earth orbit and beyond, notably the radiative environment (photons and energetic particles) and the possibility to conduct long-duration measurements, have been the main motivations for developing experimental concepts to expose chemical or biological samples to outer space, or to use the reentry of a spacecraft on Earth to simulate the fall of a meteorite. This paper represents an overview of past and current research in astrobiology conducted in Earth orbit and beyond, with a special focus on ESA missions such as Biopan, STONE (on Russian FOTON capsules) and EXPOSE facilities (outside the International Space Station). The future of exposure platforms is discussed, notably how they can be improved for better science return, and how to incorporate the use of small satellites such as those built in cubesat format.