Morality is among the most sophisticated features of human judgement, behaviour and, ultimately, mind. An individual who behaves immorally may violate ethical rules and civil rights, and may threaten others' individual liberty, sometimes becoming violent and aggressive. In recent years, neuroscience has shown a growing interest in human morality, and has advanced our understanding of the cognitive and emotional processes involved in moral decisions, their anatomical substrates and the neurology of abnormal moral behaviour. In this article, we review research findings that have provided a key insight into the functional and clinical neuroanatomy of the brain areas involved in normal and abnormal moral behaviour. The 'moral brain' consists of a large functional network including both cortical and subcortical anatomical structures. Because morality is a complex process, some of these brain structures share their neural circuits with those controlling other behavioural processes, such as emotions and theory of mind. Among the anatomical structures implicated in morality are the frontal, temporal and cingulate cortices. The prefrontal cortex regulates activity in subcortical emotional centres, planning and supervising moral decisions, and when its functionality is altered may lead to impulsive aggression. The temporal lobe is involved in theory of mind and its dysfunction is often implicated in violent psychopathy. The cingulate cortex mediates the conflict between the emotional and the rational components of moral reasoning. Other important structures contributing to moral behaviour include the subcortical nuclei such as the amygdala, hippocampus and basal ganglia. Brain areas participating in moral processing can be influenced also by genetic, endocrine and environmental factors. Hormones can modulate moral behaviour through their effects on the brain. Finally, genetic polymorphisms can predispose to aggressivity and violence, arguing for a genetic-based predisposition to morality. Because abnormal moral behaviour can arise from both functional and structural brain abnormalities that should be diagnosed and treated, the neurology of moral behaviour has potential implications for clinical practice and raises ethical concerns. Last, since research has developed several neuromodulation techniques to improve brain dysfunction (deep brain stimulation, transcranial magnetic stimulation and transcranial direct current stimulation), knowing more about the 'moral brain' might help to develop novel therapeutic strategies for neurologically based abnormal moral behaviour.