Across cultures humans care deeply about morality and create institutions, such as criminal courts, to enforce social norms. In such contexts, judges and juries engage in complex social decision-making to ascertain a defendant's capacity, blameworthiness, and culpability. Cognitive neuroscience investigations have begun to reveal the distributed neural networks which interact to implement moral judgment and social decision-making, including systems for reward learning, valuation, mental state understanding, and salience processing. These processes are fundamental to morality, and their underlying neural mechanisms are influenced by individual differences in empathy, caring and justice sensitivity. This new knowledge has important implication in legal settings for understanding how triers of fact reason. Moreover, recent work demonstrates how disruptions within the social decision-making network facilitate immoral behavior, as in the case of psychopathy. Incorporating neuroscientific methods with psychology and clinical neuroscience has the potential to improve predictions of recidivism, future dangerousness, and responsivity to particular forms of rehabilitation.