Exposure of living organisms to open space requires a high level of tolerance to desiccation, cold, and radiation. Among animals, only anhydrobiotic species can fulfill these requirements. The invertebrate phylum Tardigrada includes many anhydrobiotic species, which are adapted to survive in very dry or cold environmental conditions. As a likely by-product of the adaptations for desiccation and freezing, tardigrades also show a very high tolerance to a number of other, unnatural conditions, including exposure to ionizing radiation. This makes tardigrades an interesting candidate for experimental exposure to open space. This paper reviews the tolerances that make tardigrades suitable for astrobiological studies and the reported radiation tolerance in other anhydrobiotic animals. Several studies have shown that tardigrades can survive gamma-irradiation well above 1 kilogray, and desiccated and hydrated (active) tardigrades respond similarly to irradiation. Thus, tolerance is not restricted to the dry anhydrobiotic state, and I discuss the possible involvement of an efficient, but yet undocumented, mechanism for DNA repair. Other anhydrobiotic animals (Artemia, Polypedium), when dessicated, show a higher tolerance to gamma-irradiation than hydrated animals, possibly due to the presence of high levels of the protective disaccharide trehalose in the dry state. Tardigrades and other anhydrobiotic animals provide a unique opportunity to study the effects of space exposure on metabolically inactive but vital metazoans.