Belief that Jesus Christ was a natural union between the Flesh and the Word, thus not identical, to the divine Son of God.
Advanced by Nestorius (386–450), Patriarch of Constantinople from 428–431. The doctrine was informed by Nestorius’ studies under Theodore of Mopsuestia at the School of Antioch.
Condemned at the First Council of Ephesus in 431 and the Council of Chalcedon in 451, leading to the Nestorian Schism. Cyril of Alexandria was the led the opposition to Nestorian teaching.
Nestorius rejected the title Theotokos for the Virgin Mary, and proposed Christotokos as more suitable. Many of Nestorius’ supporters relocated to Sassanid Persia, where they affiliated with the local Christian community, known as the Church of the East. Over the next decades the Church of the East became increasingly Nestorian in doctrine, and known alternately as the Nestorian Church.
The development of a Nestorian Creed (A modified version of the Nicene Creed of Constantinople) was also condemned at the Council of Ephesus and pronounced anathemas on any who would add to or subtract from the Nicene Creed.
The principal problem with Nestorianism is that it denies the incarnation, ultimately to say that God did not become man in the way that the Gospels teach.
See Matthew 1:18-25, Luke 1:26-45, Luke 2:25-35.