The detail
After Ephesus (431), the question was no longer whether Christ is one but how to describe the union of God and man in him. Cyril of Alexandria (d. 444) had used the formula "one incarnate nature (physis) of God the Word", while also accepting, in the Formula of Reunion of 433, language about two natures. In 448 the Constantinopolitan monk Eutyches was condemned for teaching that after the union there was only one nature, apparently implying that Christ's humanity was not consubstantial with ours. A council at Ephesus in 449, presided over by Dioscorus of Alexandria, rehabilitated Eutyches and refused to read Pope Leo I's Tome; Leo called it a latrocinium, a "robber council".
The new emperor Marcian convened the Council of Chalcedon in 451. It deposed Dioscorus (formally on procedural and disciplinary grounds), received Leo's Tome, condemned Eutyches, and issued a definition confessing one and the same Christ "acknowledged in two natures, without confusion, without change, without division, without separation", the two natures concurring in one person (prosopon) and one hypostasis. Its supporters saw this as a balance between the errors attributed to Nestorius and to Eutyches.
Opponents, who were especially numerous in Egypt and among Syriac-speaking Christians, objected that "in two natures" was Nestorius's position under new words, that the council had humiliated the see of Alexandria, and that Leo's Tome spoke of each nature acting on its own. They held to "one nature" in Cyril's sense: a single, united reality of the incarnate Word, fully divine and fully human, without mixture. Modern scholars and these churches themselves prefer the term miaphysite ("one united nature") to monophysite, which suggests the humanity was absorbed; the Oriental Orthodox churches explicitly condemn Eutyches. Much of the dispute turned on terms (physis, hypostasis, prosopon) that the two sides used in different senses.
The division was also political and cultural. Emperors tried for more than a century to restore unity: Zeno's Henotikon (482) avoided Chalcedon and led to the Acacian schism with Rome (484–519); Justinian combined pressure with concessions, and the Second Council of Constantinople (553) condemned the "Three Chapters" largely to reassure the anti-Chalcedonians; Heraclius promoted monoenergism and monothelitism (630s) with the same aim. None of this worked. Under Severus of Antioch and Jacob Baradaeus (ordained bishop c. 542/543) a separate hierarchy was built, and the Arab conquests of the 630s–640s ended imperial leverage over Egypt and Syria. Armenia, which missed Chalcedon while fighting Persia at the Battle of Avarayr (451), distanced itself from the council at a synod in Dvin in 506 and formally rejected it at another Dvin synod usually dated 555 (exact dates and content are debated).
Today's Oriental Orthodox family comprises the Coptic, Syriac, Armenian Apostolic, Ethiopian, Eritrean and Malankara (Indian) Orthodox churches. In the Chalcedonian narrative (Eastern Orthodox and Catholic), these churches left the faith defined by the Fourth Ecumenical Council; in the Oriental Orthodox narrative, they kept the faith of Nicaea, Constantinople and Ephesus and of Cyril, while Chalcedon innovated. Since the 20th century dialogue has largely concluded that both confess the same reality: unofficial consultations at Aarhus (1964), Bristol (1967), Geneva (1970) and Addis Ababa (1971) led to the official Eastern Orthodox–Oriental Orthodox agreed statements of Anba Bishoy, Egypt (1989) and Chambésy, Switzerland (1990), which proposed lifting the mutual anathemas. On the Catholic side, common declarations were signed with Pope Shenouda III (1973), Syriac Patriarch Ignatius Zakka I (1984) and Armenian Catholicos Karekin I (1996). Full communion has not been restored, mainly over the status of later councils and of the saints each side condemned.