Punishment is the act of penalizing an individual as a response to a transgression. This thesis will deal with punishment in experimental game scenarios and in experimental criminal punishment scenarios, along with their different adaptations. The aim will be to provide an overview of both psychological and neurological underpinnings of punishment by reviewing existing literature. While punishment ought to deter transgressions and promote cooperative behavior, internal neural reward-related systems seem to be a driving factor of the desire to punish wrongdoings. Decisions on whether a transgressor is guilty and deserves punishment is mediated by the medial prefrontal cortex with an emphasis on the ventromedial parts. External influences affect the behavioral output and its underlying neural signatures of punishment. Social context such as peer pressure and in-group bias emphasize the importance of theory of mind related areas when conducting punishment.