Background: Three groups of children are involved in bullying: victims, bullies and bully-victims who are both bullies and victims of bullying. Understanding the origins of these groups is important since they have elevated emotional and behavioural problems, especially the bully-victims. No research has examined the genetic and environmental influences on these social roles. Method: Mother and teacher reports of victimisation and bullying were collected in a nationally representative cohort of 1,116 families with 10-year-old twins. Model-fitting was used to examine the relative influence of genetics and environments on the liability to be a victim, a bully or a bully-victim. Results: Twelve percent of children were severely bullied as victims, 13% were frequent bullies, and 2.5% were heavily involved as bully-victims. Genetic factors accounted for 73% of the variation in victimisation and 61% of the variation in bullying, with the remainder explained by environmental factors not shared between the twins. The covariation between victim and bully roles (r = 0.25), which characterises bully-victims, was accounted for by genetic factors only. Some genetic factors influenced both victimisation and bullying, although there were also genetic factors specific to each social role. Conclusions: Children's genetic endowments, as well as their surrounding environments, influence which children become victims, bullies and bully-victims. Future research identifying mediating characteristics that link the genetic and environmental influences to these social roles could provide targets for intervention.