Most human decisions are made among social others, and in what social context the choices are made is known to influence individuals' decisions. Social influence has been noted as an important factor that may nudge individuals to take more risks (e.g., initiation of substance use), but ironically also help individuals to take safer actions (e.g., successful abstinence). Such bi-directional impacts of social influence hint at the complexity of social information processing. Here, we first review the recent computational approaches that shed light on neural and behavioral mechanisms underlying social influence following basic computations involved in decision-making: valuation, action selection, and learning. We next review the studies on social influence from various fields including neuroeconomics, developmental psychology, social psychology, and cognitive neuroscience, and highlight three dimensions of determinants-who are the recipients, how the social contexts are presented, and to what domains and processes of decisions the influence is applied-that modulate the extent to which individuals are influenced by others. Throughout the review, we also introduce the brain regions that were suggested as neural instantiations of social influence from a large body of functional neuroimaging studies. Finally, we outline the remaining questions to be addressed in the translational application of computational and cognitive theories of social influence to psychopathology and health.