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'.
Ransom and Christus Victor theoryThe ransom and Christus Victor theories present Jesus as dying to overcome (supernatural) powers of sin and evil. In this model, the devil has ownership over humanity (because they have sinned) so Jesus dies in their place to free them. The doctrine is that Jesus gave himself as a ransom sacrifice in behalf of the people. (Matthew 20:28) This is known as the oldest of the theories of the atonement, and is, in some form, still, along with the doctrine of theosis, the Eastern Orthodox Church's main theory of the atonement.
Satisfaction and penal substitutionThe widest held substitutionary theory in the West is the penal substitution model. Both the penal theory and Anselm's satisfaction theory hold that only human beings can rightfully repay the debt (to God's honour [Anselm], or to God's justice [penal substitution]) which was incurred through their wilful disobedience to God. Since only God can make the satisfaction necessary to repay it, therefore God sent the God-man, Jesus Christ, to fulfil both these conditions. Christ is a sacrifice by God on behalf of humanity, taking humanity’s debt for sin upon himself, and propitiating God’s wrath.
| appease, placate, mollify, pacify, make peace with, conciliate, make amends to, soothe, calm e|
"my attempts to propitiate you are useless"
There are a number of other substitutionary theories of the atonement besides the four described above. A few are listed below:
And to whom has the arm of the Lord been revealed?
2 For he grew up before him like a young plant,
and like a root out of dry ground;
he had no form or majesty that we should look at him,
and no beauty that we should desire him.
3 He was despised and rejected[b] by men;
a man of sorrows,[c] and acquainted with[d] grief;[e]
and as one from whom men hide their faces[f]
he was despised, and we esteemed him not.
and carried our sorrows;
yet we esteemed him stricken,
smitten by God, and afflicted.
5 But he was pierced for our transgressions;
he was crushed for our iniquities;
upon him was the chastisement that brought us peace,
and with his wounds we are healed.
6 All we like sheep have gone astray;
we have turned—every one—to his own way;
and the Lord has laid on him
the iniquity of us all.
yet he opened not his mouth;
like a lamb that is led to the slaughter,
and like a sheep that before its shearers is silent,
so he opened not his mouth.
8 By oppression and judgment he was taken away;
and as for his generation, who considered
that he was cut off out of the land of the living,
stricken for the transgression of my people?
9 And they made his grave with the wicked
and with a rich man in his death,
although he had done no violence,
and there was no deceit in his mouth.
he has put him to grief;[g]
when his soul makes[h] an offering for guilt,
he shall see his offspring; he shall prolong his days;
the will of the Lord shall prosper in his hand.
11 Out of the anguish of his soul he shall see[i] and be satisfied;
by his knowledge shall the righteous one, my servant,
make many to be accounted righteous,
and he shall bear their iniquities.
12 Therefore I will divide him a portion with the many,[j]
and he shall divide the spoil with the strong,[k]
because he poured out his soul to death
and was numbered with the transgressors;
yet he bore the sin of many,
and makes intercession for the transgressors.