Nestorianism

Nestorianism is the belief, originated by Nestorius, the Patriarch of Constantinople (briefly), that Christ was of two distinct hypostases or natures, one human and one divine. Like most early disputes over Christology, it ended with excommunications being handed out like candy.

Origins to schism
Nestorius was taught theology at the distinctly literalist School of Antioch, which emphasised the distinctiveness of Christ's human and divine natures. From there, he went on to be appointed Patriarch of Constantinople by Theodosius II in 428. Once in office, he waged a zealous campaign against Arians, Macedonians (the sect, not the nationality), Novatians, and other varieties of heretic, before himself causing an uproar by arguing that the traditional title Theotokos (literally "bringer forth of God") should not be used for Mary, as it failed to recognize Jesus's human nature, and suggested the title Christotokos instead. This reeked of adoptionism to many, and the Patriarch of Alexandria and the Pope both became involved against the idea of Christ's natures being so loosely united as Nestorius proposed.

Schism and Church of the East
In 431 the emperor Theodosius II convened an ecumenical council to resolve the issue: the First. Though some at the council initially spoke out in favor of Nestorius, the political winds blew as they do, and his teachings were ultimately anathemised. Sound familiar? Afterwards, many Christians who still faithfully held to the Nestorian position fled from the Roman Empire to Sassanid Persia, and in 486 the, which had previously renounced foreign authority (i.e. the Pope etc.), officially adopted Nestorius's teachings. From Persia, in a classic example of (temporarily) successful evangelism, Nestorianism spread across Asia, reaching as far as Mongolia, China, and India at the height of its influence in the Middle Ages, before falling apart into a number of sects, some of which returned to communion with Rome.