Perovskites have emerged as promising light harvesters in photovoltaics. The resulting solar cells (i) are thin and lightweight, (ii) can be produced through solution processes, (iii) mainly use low-cost raw materials, and (iv) can be flexible. These features make perovskite solar cells intriguing as space technologies; however, the extra-terrestrial environment can easily cause the premature failure of devices. In particular, the presence of high-energy radiation is the most dangerous factor that can damage space technologies. This Review discusses the status and perspectives of perovskite photovoltaics in space applications. The main factors used to describe the space environment are introduced, and the results concerning the radiation hardness of perovskites toward protons, electrons, neutrons, and γ-rays are presented. Emphasis is given to the physicochemical processes underlying radiation damage in such materials. Finally, the potential use of perovskite solar cells in extra-terrestrial conditions is discussed by considering the effects of the space environment on the choice of the architecture and components of the devices.