Nestorianism is a movement within Christianity. The idea behind the doctrine was that there were two different persons of Jesus. One of them was the man Jesus, the other was the aspect of son of God, or Logos. Perhaps the most prominent supporter of the idea was Nestorius, archbishop of Constantinople. Nestorius lived from about 380 to about 450 AD. The Council of Ephesus condemned this view in 431. This led to a split of the church, into the Assyrian Church of the East and the Byzantine Church.
For this reason, the Assyrian Church of the East is sometimes called Nestorian. The church holds the view that Christ has two essences (qnome) that are united in one person (parsopa).
The only two churches that teach Nestorianism today are the Assyrian Church of the East, and the Church of the East & Abroad.