In farm animal breeding, behavioural traits are rarely included in selection programmes despite their potential to improve animal production and welfare. Breeding goals have been broadened beyond production traits in most farm animal species to include health and functional traits, and opportunities exist to increase the inclusion of behaviour in breeding indices. On a technical level, breeding for behaviour presents a number of particular challenges compared to physical traits. It is much more difficult and time-consuming to directly measure behaviour in a consistent and reliable manner in order to evaluate the large numbers of animals necessary for a breeding programme. For this reason, the development and validation of proxy measures of key behavioural traits is often required. Despite these difficulties, behavioural traits have been introduced by certain breeders. For example, ease of handling is now included in some beef cattle breeding programmes. While breeding for behaviour is potentially beneficial, ethical concerns have been raised. Since animals are adapted to the environment rather than the other way around, there may be a loss of 'naturalness' and/or animal integrity. Some examples, such as breeding for good maternal behaviour, could enhance welfare, production and naturalness, although dilemmas emerge where improved welfare could result from breeding away from natural behaviour. Selection against certain behaviours may carry a risk of creating animals which are generally unreactive ('zombies'), although such broad effects could be measured and controlled. Finally, breeding against behavioural measures of welfare could inadvertently result in resilient animals ('stoics') that do not show behavioural signs of low welfare yet may still be suffering. To prevent this, other measures of the underlying problem should be used, although cases where this is not possible remain troubling.