This paper considers neurocognitive models of aggression and relates them to explanations of the antisocial personality disorders. Two forms of aggression are distinguished: reactive aggression elicited in response to frustration/threat and goal directed, instrumental aggression. It is argued that different forms of neurocognitive model are necessary to explain the emergence of these different forms of aggression. Impairments in executive emotional systems (the somatic marker system or the social response reversal system) are related to reactive aggression shown by patients with "acquired sociopathy" due to orbitofrontal cortex lesions. Impairment in the capacity to form associations between emotional unconditioned stimuli, particularly distress cues, and conditioned stimuli (the violence inhibition mechanism model) is related to the instrumental aggression shown by persons with developmental psychopathy.