While Nestorian is the term popular amongst the West, it is actually considered a pejorative term amongst Assyrians (a bit like calling Catholics Papists). Anyway, the Assyrian Church of the East has existed since the beginning and tradition says it was established by the Apostle Thomas. The Assyrian Church is still extant today and it additionally has an Eastern Catholic counterpart sui iuris Church (the Chaldeans).
The Assyrian Church is an East Syriac Church (I am, for example, from a West Syriac Church established in Syria, but the East Syriacs are from the Mesopotamian area). Both the West and East Syriacs have essentially lived under Islamic reign since the Islamic invasions (both under the Caliphate then the West Syriacs were later under the Ottoman Turks and the East Syriacs under Persian rule). In its heydays it had churches stretching from modern day Iraq all the way to China and India (where there are still remnants - the Syro-Malabars). Although it has been an arduous trial God sustains us. It truly is a miracle we still exist, although nowadays we’re staggering.
The Assyrian Church does indeed have descendants til this day. It has about 500k adherents, is headquartered in Chicago and has churches around the US and the world. Christianity in the Middle East, especially Iraq, is on the brink of extinction sadly… Especially thanks to a certain American president’s war.
Edit: I should make it clear that the term Nestorian is a misnomer because Assyrians, despite venerating Nestorius as a saint, do not believe in the heresy ascribed to him by the West.
No offense, but you should look at existing threads on a topic before starting a new one. If you had, you would have seen that the ACoE (Assyrian Church of the East) does not practice the “Nestorian” heresy. :o
Not too long ago, while thinking about all that, I got to wondering whether those 15,000 or so ACoE-in-India (the Chaldean-Syrian Church if anyone reading this is a stickler for names ;)) might “merge back into” the Syro-Malabar Catholic Church … but then I put the idea aside as unecumenical. (I suppose might ask “If it’s unecumenical, why even bring it up?”)