Unchecked aggression and violence exact a significant toll on human societies. Aggression is an umbrella term for behaviours that are intended to inflict harm. These behaviours evolved as adaptations to deal with competition, but when expressed out of context, they can have destructive consequences. Uncontrolled aggression has several components, such as impaired recognition of social cues and enhanced impulsivity. Molecular approaches to the study of aggression have revealed biological signals that mediate the components of aggressive behaviour. These signals may provide targets for therapeutic intervention for individuals with extreme aggressive outbursts. This Review summarizes the complex interactions between genes, biological signals, neural circuits and the environment that influence the development and expression of aggressive behaviour.