After the disputes of the fifth century, how were 'Nestorians' viewed in the West? Within the (Eastern) Roman empire, a lot of time was spent on the argument between Chalcedonians and non-Chalcedonians, but Christians in the post-Roman West largely did not have to deal with that - how then did they characterise the Church of the East, and how accurate was their knowledge given the distance between them?
Great question! I've just been reading some of the correspondence between Fulgentius of Ruspe, a North African bishop exiled to Sicily by the Arian king in Africa and a spiritual heir of Augustine, and a group of Scythian monks concerned about a lack of clarity in the Chalcedonian definition against Nestorianism. The West was not very involved with the controversy, with the exception of the Tome of Pope Leo which was officially ratified at Chalcedon and marks the first time a Bishop of Rome played a major role in an ecumenical council. Augustine in particular never wrote specifically on Christology, being so focused on the Donatist and Pelagian controversies, and the little Christology that peeks through in his writings on Predestination show some rather, shall we say, vague terminology.
However, Fairbairn has demonstrated pretty well that there was a broad consensus in the West and East that the anti-Nestorian Christology of Cyril of Alexandria was correct, and Nestorius' doctrine was not supported in the West.
In the early 5th century, in Augustine's day, there wasn't a lot of clarity on the Eastern issues, but by the 6th century Fulgentius seems pretty aware of what's going on. Prosper of Aquitaine also wrote an interesting verse about Arians and Nestorians as sisters in heresy. John Cassian, though, does seem a little unclear sometimes about Nestorians, though he still says he rejects their doctrine. So it wasn't a huge issue in the West but by the 6th century they generally knew what was going on, and sided with Chalcedon. Of course the Pope sided strongly with Chalcedon because it bolstered his own authority! The Eastern Emperor Zeno published his Henotikon as an attempt at compromise, but it wasn't backed in the West because unlike Chalcedon ratifying Leo's Tome, it didn't lend credence to the papal position.
Grace and Christology by Donald Fairbairn
Fulgentius of Ruspe: Correspondence on Christology and Grace, Fathers of the Church series vol. 126, trans. McGregor and Fairbairn.
John Cassian, Nicene and Post-Nicene Fathers, series 2, vol. 11, especially Seven Books on the Incarnation.