Psychopathy is a core topic of neurobiological research on criminal behavior. This article contains a brief overview on the state of knowledge in this field. Although Hare's (1991) concept of psychopathy and the PCL-R contributed much to sound research, various problems suggest that more recent multidimensional concepts should be included. It is also shown that the PCL-R is not a better predictor of general and violent recidivism than other structured risk assessment instruments. The core part of the article addresses neurobiological theories and findings on psychopathy. Research suggests that psychopaths show deviant levels in physiological, hormonal and neurotransmitter characteristics and, in particular, deficits in the functioning of the prefrontal cortex and the limbic system. Such findings fit to theories of deficits in cortical arousal, avoidance learning, somatic markers, emotionality, empathy, self-control, and attention modulation. In addition to progress in basic research on psychopathy there is also some promising development with regard to the treatment and management of psychopaths. Research deficits and future perspectives are briefly outlined.