A brief history of Christian atonement thought
Christ is primarily seen as a teacher of virtue and monotheism. By hearing and following Christ's teachings and example, Christian converts are able to turn from their old sinful ways and live righteously before God. Some also add teaching of Recapitulation, or Christus Victor/Ransom-from-Satan (CV/RS). No original sin. Final judgement by works. Free Will.
250-500AD, Original Sin in the West
The doctrine of Original Sin develops in North Africa. Pelagius, Augustine, Cassian, between them result in Western Christianity adopting a significantly more pessimistic view of man than Eastern Christianity. Augustine invents the idea of Predestination, but it is not very influential.
350+, A not-so Eternal Hell in the West
In discussion of whether hell is eternal, or whether God might eventually bring hell to an end, it is suggested that perhaps hell is not eternal for Christians who are sent to hell (for their evil works). Western Christianity adopts the idea that for evil Christians hell is not eternal. This leads to it becoming "Purgatory". Thus, Christians unworthy to go to heaven go to purgatory temporarily, prior to heaven.
313-1000AD Atonement Models
In Eastern Christianity the atonement model of Christ-as-teacher merges with the model of Recapitulation to produce "Theosis", which is about both sanctification and ontological transformation (ie humanity becomes 'divine' by becoming godly and virtuous, and also by spiritually 'participating' in God). CV/RS and Theosis both universally taught in East. The East then goes largely into doctrinal stasis.
In Western Christianity the atonement models in use are Christ as teacher of righteousness, CV/RS, and an emerging new idea that conceived of Christ's work as targeted at God and as a gift to him. CV/RS is universally dominant over this period, with Christ as teacher being taken for granted, and Christ-as-gift cropping up occasionally.
1100+AD New and Old Models in the West
In Western Christianity, Anselm challenged CV/RS and drew up a formal version of the Christ-as-gift theory to replace it, which became known as "Satisfaction". The offense given to God by human disobedience was made up for by Christ's faithful obedience to God. Peter Abelard objected vigorously to Anselm's ideas, but rather than defend CV/RS against Anselm's challenge he attempted to reinvigorate the Christ-as-Teacher model, which became known as "Moral Exemplar". Western Christianity from this point on generally dropped CV/RS and became split between Satisfaction and Moral Exemplar
1400-1700 Satisfaction gets a face lift
Anselm's satisfaction model was based on the idea of God as a Feudal Lord and acting according to social norms in accepting Christ's faithfulness as repayment for our disobedience. As society passed out of feudalism his ideas were recast using a paradigm of a Law-Court: "Penal Substitution" (PS). This added to Satisfaction the idea of Christ suffering our punishment. A modified form of PS that was popular for a while was the "Governmental View" which attempts to drop some of the conceptual difficulties inherent in the original.
1500+ Reformation Theology in the West
The Reformers adopted wholehearted the Penal Substitution theology of their day. Original Sin was strengthened by them back to Augustine's levels. Augustine's predestination ideas were reintroduced. Salvation was by "faith alone" and all works were moved into the category of "sanctification" which was made tangential to the main salvation process. "Justification" was redefined, no longer being about inner moral transformation, and now considered to mean a righteous status declared by God that was contrary to our real state of sinfulness.
1700-2000 To the Present Day
The Eastern Orthodox continued to hold their Theosis and CV/RS views. They still endorsed free will, rejected original sin, and held to final judgment by works.
Conservative Protestants and Roman Catholics continued to endorse and defend their party lines. Liberal Protestants held the Moral Exemplar view and free will and rejected original sin. Within conservative protestantism the Arminians and Calvinists debated their differences on free will, while the Catholics and Protestants debated their differences on the nature of justification and faith/works, and the conservatives and liberals debated over Penal Substitution and Moral Exemplar.