Substitutionary atonement, also called vicarious atonement, is a central concept within Western Christian theology which asserts that Jesus died for humanity, as claimed by the Western classic and paradigms of atonement in Christianity, which regard Jesus as dying as a substitute for others.

Substitutionary atonement has been explicated in the "classic paradigm" of the Early Church Fathers, namely the ransom theory, as well as in Gustaf Aulen's demystified reformulation, the Christus Victor theory; and in the "objective paradigm," which includes Anselm of Canterbury's satisfaction theory, the Reformed period's penal substitution theory, and the Governmental theory of atonement.

Substitutionary atonement, also called vicarious atonement, is the idea that Jesus died "for us". There is also a less technical use of the term "substitution" in discussion about atonement when it is used in "the sense that [Jesus, through his death,] did for us that which we can never do for ourselves".

The English word atonement originally meant "at-one-ment", i.e. being "at one", in harmony, with someone. According to Collins English Dictionary, it is used to describe the redemption through Jesus' death and resurrection, to reconcile the world to himself, and also of the state of a person having been reconciled to God.

The word "atonement" is often used in the Old Testament to translate the Hebrew words kipper and kippurim, which mean 'propitiation' or 'expiation'. The word occurs in the KJV in Romans 5:11 and has the basic meaning of reconciliation. In the Old Testament (Hebrew Bible or Tanakh), atonement was accomplished by the sacrifice of specified animals such as lambs to pay for one's sins.

A distinction has to be made between substitutionary atonement (Christ suffers for us), and penal substitution (Christ punished instead of us), which is a subset or particular type of substitutionary atonement. Care should be taken when one reads the language of substitution in, for example, patristic literature, not to assume any particular substitution model is being used but should, rather, check the context to see how the author was using the language.

According to Pate, the Jewish scriptures describe three types of vicarious atonement: the Paschal Lamb although the Paschal Lamb was not a sin offering; "the sacrificial system as a whole", although these were for "mistakes", not intentional sins and with the Day of Atonement as the most essential element; and the idea of the suffering servant (Isaiah 42:1-9, 49:1-6, 50:4-11, 52:13-53:12). The Old Testament Deuterocanon added a fourth idea, namely the righteous martyr (2 Maccabees, 4 Maccabees, Wisdom 2-5).

These traditions of atonement offer only temporary forgiveness, and korbanot (offerings) could only be used as a means of atoning for the lightest type of sin, that is sins committed in ignorance that the thing was a sin. In addition, korbanot have no expiating effect unless the person making the offering sincerely repents his or her actions before making the offering, and makes restitution to any person who was harmed by the violation. Marcus Borg notes that animal sacrifice in Second Temple Judaism was not a "payment for sin," but had a basic meaning as "making something sacred by giving it as a gift to God," and included a shared meal with God. Sacrifices had numerous purposes, namely thanksgiving, petition, purification, and reconciliation. None of them were a "payment or substitution or satisfaction," and even "sacrifices of reconciliation were about restoring the relationship."