There is continuing debate over whether bilingualism can confer advantages in other areas of cognition. Bilingual language behaviours, such as switching between languages, are often assumed to engage domain-general executive functions that control and regulate behaviour. According to this account, language switching might also improve executive functions used for nonverbal tasks. An alternative account suggests that bilingual language behaviours are skills that become automatic with practice and come to rely on task-specific processes instead of domain-general executive functions. According to this account, repeated training in bilingual language behaviours would not enhance executive functions generally. In this Review, we examine cross-sectional and longitudinal research on language switching and executive function in language users with and without cognitive deficits in order to compare the domain-generality and skill-learning accounts. We also discuss how these results converge with the findings of task specificity in the cognitive training literature suggesting that training does not generalize to other tasks. We hope to stimulate further research contrasting these two accounts, with the goal of a better understanding of the relationship between bilingualism and cognitive control and whether it is possible to train executive functions via bilingual language behaviours.