Chalcedonian Christianity

Chalcedonian Christianity refers to the branch of Christianity that accepts and upholds theological and ecclesiological resolutions of the Council of Chalcedon, the Fourth Ecumenical Council, held in 451. Chalcedonian Christianity accepts the Christological Definition of Chalcedon, a Christian doctrine concerning the union of two natures (divine and human) in one hypostasis of Jesus Christ, who is thus acknowledged as a single person (prosopon). Chalcedonian Christianity also accepts the Chalcedonian confirmation of the Niceno-Constantinopolitan Creed, thus acknowledging the commitment of Chalcedonism to the Nicene Christianity. 
In regard to their specific attitudes towards theological resolutions of the Council of Chalcedon, Christian denominations (both historical and modern) can be divided into:
History.
The dogmatic disputes raised during the Council of Chalcedon led to the Chalcedonian Schism thus to the formation of the Non-Chalcedonian body of churches known as Oriental Orthodoxy. The Chalcedonian churches remained united with the Holy See of Rome, the Ecumenical Patriarchate of Constantinople (or "New Rome") and the Eastern Orthodox patriarchates of the Middle East (namely Alexandria, Antioch and Jerusalem). Together, these five patriarchates were considered the pillars of orthodox catholic Christendom and of the Chalcedonian confession of faith. During the 6th-century reign of Emperor Justinian I, the five patriarchates were recognised as the Pentarchy, the official ecclesiastical authority of the Imperial Christian Church.
Pre-Chalcedonian Christianity was mainly based on Paul. John of Tella described the foundations of pre-Chalcedeonian Christianity:
And [the council of Nicaea] considered and saw widely where it set up its building; and the divine Paul, wise among spiritual master-builders, invoked them, and showed them the true foundation, a rock that can not be shaken; on it they will place and build their building; and those he spoke before them when he was saying: Another foundation except for you this you should not constitute, this is Jesus Christ; it was on this that Simeon built and John; on it that Thomas completed [his mission] in Cush. And in Egypt Mark built upon it, and Addai the house of the Medians, Persians and Parthians. And it was on this that the apostle Matthew built in Palestine, and Jacob, the brother of our Lord.
He believed this foundation was abandoned at Chalcedon: "the council of Chalcedon builds not at all on the foundation that the divine master-builder Paul has set up, but on the sand that Nestorius, the confused and dethroned builder, put to it".
Today, the great majority of Christian denominations can be considered descended from the Pentarchy, subscribing to Chalcedonian Christianity, broadly divided into the Roman Catholic Church in the predominantly Latin-speaking West, the Eastern Orthodox Church in the predominantly Greek-speaking East, and the Protestant denominations created in the wake of the Protestant Reformation.
The groups that rejected Chalcedon's Christological definition were the majority of the Armenian, Coptic, and Ethiopian Christians, together with a part of the Indian and Syriac Christians (the latter of which came to be identified as "Jacobites"). Today, such groups are known collectively as the Non-Chalcedonian, Miaphysite, or Oriental Orthodox churches.
Some Armenian Christians, especially in the region of Cappadocia and Trebizond inside the Byzantine Empire, accepted the decisions of the Council of Chalcedon and engaged in polemics against the Armenian Apostolic Church.
After the conclusion of Byzantine-Sasanian War of 572–591, direct rule of the Byzantine Empire was extended to all western parts of Armenia, and soon after that emperor Maurice (582–602) decided to strengthen his political control over the entire region by supporting the local pro-Chalcedonian faction of the Armenian Church. In 593, a regional council of western Armenian bishops was convened in the city of Theodosiopolis, and proclaimed allegiance to the Chalcedonian Definition. 
The council also elected John (Yohannes, or Hovhannes) of Bagaran as the new Catholicos of the Chalcedonian Armenians.
Chalcedonian Christology.
Those present at the Council of Chalcedon accepted Trinitarianism and the concept of hypostatic union, and rejected Arianism, Modalism, and Ebionism as heresies (which had also been rejected at the First Council of Nicaea in AD 325). Those present at the council also rejected the Christological doctrines of the Nestorians, Eutychians, and monophysites (these doctrines had also been rejected at the First Council of Ephesus in 431).
The Chalcedonian understanding of how the divine and human relate in Jesus Christ is that the humanity and divinity are exemplified as two natures and that the one hypostasis of the "Logos" perfectly subsists in these two natures. The Non-Chalcedonians hold the position of miaphysitism (sometimes called monophysitism by their opponents). Miaphysitism holds that in the one person of Jesus Christ, divinity and humanity are united in one nature, the two being united without separation, without confusion and without alteration. That led many members of the two churches to condemn each other: the Chalcedonians condemning the Non-Chalcedonians as Eutychian Monophysites, and the Non-Chalcedonians condemning the Chalcedonians as Nestorians.
Later interpreters of the council held that Chalcedonian Christology also rejected monothelitism and monoenergism (rejected at the Third Council of Constantinople in 680). Those who did not accept the Chalcedonian Christology now call themselves "non-Chalcedonian". Historically, they called themselves Miaphysites or Cyrillians (after St Cyril of Alexandria, whose writing "On the Unity of Christ" was adopted by them and taken as their standard) and were called by Orthodox Christians monophysites. Those who held to the non-Chalcedonian Christologies called the doctrine of Chalcedon "dyophysitism".