After the Council of Ephesus (431), the Church of Seleucia-Ctesiphon, which had hitherto been governed by a catholicos under Antioch, refused to accept the condemnation of Nestorius, cut itself and the Church to the East of it off from the Catholic Church. In 498 the catholicos assumed the title of "Patriarch of the East", and for many centuries this most successful missionary church continued to spread throughout Persia, Tartary, Mongolia, China, India, developing on lines of its own, very little influenced by the rest of Christendom. At the end of the fourteenth century the conquests of Tamerlane all but destroyed this flourishing Church at one blow, reduced it to a few small communities in Persia, Turkey in Asia, Cyprus, South India, and the Island of Socotra. The Cypriote Nestorians united themselves to Rome in 1445; in the sixteenth century there was a schism in the patriarchate between the rival lines of Mar Shimun and Mar Elia; the Christianity of Socotra, such as it was, died out about the seventeenth century; the Malabarese Church divided into Catholics and Schismatics in 1599, the latter deserting Nestorianism for Monophysitism and adopting the West Syrian Rite about fifty years later; in 1681 the Chaldean Unia, which had been struggling into existence since 1552, was finally established, and in 1778 received a great accession of strength in the adhesion of the whole Mar Elia patriarchate, and all that was left of the original Nestorian Church consisted of the inhabitants of a district between the Lakes of Van and Urmi and Tigris, and outlying colony in Palestine. These have been further reduced by a great massacre by the Kurds in 1843, and the secession of a large number to the Russian Church within the last few years. In the late nineteenth century there was an attempt to form an "Independent Catholic Chaldean Church", on the model of the "Old Catholics". This resulted in separating a few from the Eastern Rite Catholics.
From the Catholic Encyclopedia
http://www.newadvent.org/cathen/14413a.htm