Consistent inter-individual variation in behaviour over time and across contexts has been reported for a wide variety of animals, a phenomenon commonly referred to as personality. As behavioural patterns develop inside families, rearing conditions could have lasting effects on the expression of adult personality. In species with parental care, conflicts among family members impose selection on parental and offspring behaviour through coadaptation. Here, we argue that the interplay between the evolution of personality traits (i.e. boldness, exploration, activity, aggressiveness and sociability) expressed outside the family context and the specialized behaviours expressed inside families (i.e. offspring begging behaviour and parental response to offspring solicitations) can have important evolutionary consequences. Personality differences between parents may relate to the typically observed variation in the way they respond to offspring demand, and dependent offspring may already express personality differences, which may relate to the way they communicate with their parents and siblings. However, there has been little research on how personality relates to parental and offspring behaviours. Future research should thus focus on how and why personality may be related to the specialized parent and offspring behaviour that evolved as adaptations to family life.