Penal substitution (sometimes, esp. in older writings, called forensic theory) is a theory of the atonement within Protestant Christian theology, which declares that Christ, voluntarily submitting to God the Father's plan, was punished (penalized) in the place of sinners (substitution), thus satisfying the demands of justice so God can justly forgive sins making us at one with God (atonement). It began with the German Reformation leader Martin Luther and continued to develop within the Calvinist tradition as a specific understanding of substitutionary atonement. The penal model teaches that the substitutionary nature of Jesus' death is understood in the sense of a substitutionary fulfilment of legal demands for the offenses of sins.
The penal substitution theory teaches that Jesus suffered the penalty due according to God the Father's wrath for humanity's sins. Penal substitution derives from the idea that divine forgiveness must satisfy divine justice, that is, that God is not willing or able to simply forgive sin without first requiring a satisfaction for it. It states that God gave himself in the person of his Son, Jesus Christ, to suffer the death, punishment and curse due to fallen humanity as the penalty for our sin.
Important theological concepts about penal substitution depend on the doctrine of the Trinity. Those who believe that Jesus was himself God, in line with the doctrine of the Trinity, believe that God took the punishment upon himself rather than putting it on someone else. In other words, the doctrine of union with Christ affirms that by taking the punishment upon himself Jesus fulfils the demands of justice not for an unrelated third party but for those identified with him. If, in the penal substitution understanding of the atonement, the death of Christ deals with sin and injustice, his resurrection is the renewal and restoration of righteousness.