Introduced cats (Felis catus) and European red foxes (Vulpes vulpes) have caused the precipitous decline and extinction of many native mammal species in Australia. Many surviving species now persist in the wild only on predator-free islands and in small natural refugia where introduced predators are at low density. These natural refugia have inspired the creation of ‘safe havens’: areas where populations of imperilled mammals can be protected from introduced predators, either on offshore islands, or by predator-proof fences on the mainland.