Many European politicians, managers, and scientists believe that non-indigenous species cannot be eradicated and that attempts to do so are hazardous because of frequent undesirable results. This notion seems to be based on the view that successful eradications undertaken in many other parts of the world cannot be generalised. To allow reasoned consideration of this argument, the eradication of non-indigenous vertebrate species performed in the French territories (European and overseas) and their recorded consequences on native fauna and flora are synthesised. Nineteen vertebrate eradication attempts were recorded, with seven mammal species as the targets. Of these attempts four failed for technical reasons and one for reasons undetermined as yet. These operations took place on islands of four biogeographical areas (West-European, Mediterranean, West Indies and Indian Ocean subantarctic) except a continental one (West-European continent). Among these 19 attempts, 13 were conducted according to a global strategy that provided data on the impact of the disappearance of the non-indigenous species on several native species. This impact, never detrimental, was determined for 14 species (one mammal, nine birds, one marine turtle, one crab, one beetle, one plant). Unexpected consequences of the disappearance of the invader were recorded for four native species (29%). This result highlights the poverty of natural historical information for several taxa and the flimsiness of the empty niche concept that is often used to argue for the delay of or to prevent any action again a non-indigenous species. If French territories can be taken as an example, eradications of non-indigenous species are not impossible; a good risk assessment prevents undesirable long-term consequences for native species and several native species benefited from the disappearance of the invader. Furthermore, eradication constitutes a powerful experimental tool for ecology and natural history studies if conceived as both a management and research operation.