This paper summarises recent findings on the causation of stereotypic behaviours and other abnormal repetitive behaviours (ARBs) in captive animals: primarily motivational frustration and/or brain dysfunction, with possible contributory roles also being played by habit-formation and ‘coping’ effects. We then review the extent to which ARBs occur in zoos and similar, estimating that at least 10 000 captive wild animals are affected worldwide. We argue for ‘zero tolerance’ of such ARBs, because stress and poor welfare raise ethical issues, while abnormal behavioural phenotypes and possibilities of impaired brain development challenge both the indirect (e.g. educational) and the direct, intrinsic conservation value of affected animals. We then consider five potential means by which ARBs may be tackled: genetic selection; pharmacological treatment; the reinforcement of alternative behaviours; punishment; and environmental enrichment. All except punishment have potentially useful roles to play, but enrichment is the preferred approach: it is most likely to tackle the problems underlying stereotypic behaviours, and thence to improve both welfare and behaviour with few unwanted side-effects. Nevertheless, in zoos, environmental enrichment to date has only had partial success, with no study managing to abolish ARBs in all its subjects—suggesting either that the enrichments currently being used are never quite optimal, or that by the time they are tackled, ARBs have become resistant to change. We suggest some ways in which the effectiveness of enrichments may be enhanced; propose that certain properties of ARBs may usefully help evaluate their likely ‘treatability’; and emphasise that if improving welfare is more important than just reducing ARB, then additional measures are needed in order to first, reliably identify those individuals most at risk from poor welfare, and then, to fully evaluate the welfare impact of enrichments. This paper also emphasises, with examples, the enormous potential value of zoo-derived data for helping understand how taxon, ecological niche, rearing history, and current housing together affect animals’ responses to captivity.