The atonement theories did not appear together; each answered a problem the previous one had left open, and setting them in sequence explains the tradition's shape better than treating them as a menu.
The earliest language is victory over hostile powers, death, sin, the devil, developed by Irenaeus in the second century as recapitulation: Christ retraces Adam's course and reverses it at every point. Origen and, later, Gregory of Nyssa pressed the image toward a transaction, a ransom paid to the devil who held a claim over humanity; Gregory of Nazianzus objected that the devil is owed nothing, and the ransom language faded as a literal claim while surviving as metaphor.
Anselm's Cur Deus Homo (about 1098) replaced the devil's claim with an offense against God's honor: sin is a debt only a God-man can pay, because the debt is infinite and only a human owes it. Abelard, writing shortly after, argued instead that the cross works by revealing God's love and moving the sinner to answering love, a moral influence account later revived by nineteenth-century liberal theology.
The Reformers took Anselm's structure and recast the currency from honor to penal law: Christ bears the punishment sin deserves, satisfying justice rather than honor, the theory now called penal substitution. Hugo Grotius proposed a further variant in the seventeenth century, that the cross upholds God's moral government by demonstrating the seriousness of sin.
Gustaf Aulen's 1930 book Christus Victor argued that the early victory motif had been wrongly treated as primitive and unsystematic, and named it a coherent third type alongside the Latin (satisfaction and penal) and subjective (moral influence) types, a classification still used in comparing the theories today.