Geoconservation is an increasingly widely adopted theoretical, practical and administrative approach to the protection of geological and geomorphological features of special scientific, functional, historic, cultural, aesthetic, or ecological value. Protected sites on Earth include natural rocky outcrops, shorelines, river banks, and landscapes, as well as human-made structures such as road cuts and quarries exposing geological phenomena. However, geoconservation has rarely been discussed in the context of other rocky and icy planets, rings, moons, dwarf planets, asteroids, or comets, which present extraordinarily diverse, beautiful, and culturally, historically and scientifically important geological phenomena. Here we propose to adapt geoconservation strategies for protecting the geological heritage of these celestial bodies, and introduce the term ‘exogeoconservation’ and other associated terms for this purpose. We argue that exogeoconservation is acutely necessary for the scientific exploration and responsible stewardship of celestial bodies, and suggest how this might be achieved and managed by means of international protocols. We stress that such protocols must be sensitive to the needs of scientific, industrial, and other human activities, and not unduly prohibitive. However, with space exploration and exploitation likely to accelerate in coming decades, it is increasingly important that an internationally agreed, holistic framework be developed for the protection of our common ‘exogeoheritage’.