A climate-driven global redistribution of species is currently underway. As species alter their geographical distributions under climate change, many will not only cross into new habitats but also new geopolitical areas. In this Perspective, we discuss the historical archetypes of managing species redistribution-persecution, protection or ignorance-which points to diverse decisions and outcomes based on a balance of societal and ecological valuation. We build the case for increasing transboundary monitoring and management of species, and for shared governance agreements that are global in scope, consisting of legally binding and biologically defensible contracts among partner countries, in what would be a critical step for the future conservation of all species.