Aggression, an overt behaviour with the intention to inflict damage, is a physiological trait with important roles throughout evolution, both in defence and predation. However, when expressed in humans in the wrong context, aggression leads to social maladjustment and crime. This special issue is about the genetic and neurobiological basis for aggression. Most of the 12 works presented here have been prepared by members of five international consortia established under the auspice of the FP7 and H2020 programs of the European Union to investigate different aspects of aggression and related behavioural phenotypes, including delineation of subtypes, aetiological mechanisms, neurobiology, neuroimaging, biomarkers, animal models and development and assessment of new treatments. Research on human aggression has largely focused on the societal causes of violent behaviour with relatively little focus on the underlying neuroscientific basis. However, interesting findings are emerging which suggest that by identifying distinct pathways to aggression, better targeting of social, psychological and medical treatments, can lead to improved outcomes for individuals and society. This issue represents a state of the art review of current neurobiological understanding of human aggression and a starting point for concerted efforts to move the field towards the development of new strategies for prevention and treatment.