I seem to always need to give an introduction or, as I sometimes say, "set it up." Over fifty years of writing sermons creates a habit that is hard to break. So allow me an introduction to this topic of atonement. Presentation of actual theories will follow over the next several days.
An effort to understand what happened when Jesus was crucified and its effect on humanity began long before the word atonement came into play. The word was coined in the 16th century. Atonement (at-one-ment) means joining into one or reconciliation. In time it came to describe what "had to be done" to effect humanity's reconciliation with God. Paul Tillich would say that atonement involves both a divine act and a human reaction.
Some will see Adam and Eve as historical characters who, because of their disobedience, caused all humanity to be infected with the reality of sin. This is most often referred to as "original sin." Others, like myself, see Adam and Eve as mythic and, thus, a kind of "Everyperson" - we see our story in their story. They disobeyed; we do the same. Sin became their reality; so it is ours. In time this came to be described as "the fall." According to this idea, everyone, including the new-born infant, is immediately stained with sin. The very act of propagation carries it forward. (In my opinion, the terms original sin and fall need some re-thinking also, but that is another effort for another day.)
In various ways, the debate on these theories seem to heat up in the middle ages. There are several and they basically coexist in Christian thought today, despite their incompatability with each other. It seems to boil down to this: All humans have sinned, a price must be paid for wrong-doing, God's holiness and justice must somehow be honored, Jesus became a substitute for us and took on the punishment that we deserved, we need Jesus to intercede for us with God, and the anger of God awaits all who resist and question this.
In thinking this through, it seems as though Jesus never really addressed something like this. This came from others (early on, think Paul). The major problem with these theories is not that they do not come from Jesus but rather what they imply about God.
Some scholars say that there are only really three theories when all thoughts are put on the table. Others believe this fans out into five or six theories. Some hold to as many as ten. I will address the traditional ones by name and in this order: Ransom, Satisfaction, Substitution, Christus Victor, and the Moral Theory. Following presentation of these traditional thoughts, I will consider two others that have developed more recently and could be considered post-modern.
I will try to get at the heart of these different theories in as brief a writing as possible. If you want to study them more in depth, the internet holds all kinds of possibilities.