Today in the Maronite calendar is the memorial of the Holy Fathers of the Council of Chalcedon. To understand the Council of Chalcedon, one must know something about Eutychianism.
Eutyches was a priest of Constantinople, an archimandrite in charge of an important monastery, who had attended the ecumenical Council of Ephesus (431). He was a firm opponent of Nestorianism and advocate of the conciliar definitions, and at some point argued things that were taken as suggesting that Christ was not consubstantial with us, that his humanity was not the same as ours. (We don't actually know for sure what his precise position was.) He was condemned at a synod held by St. Flavian, the Patriarch of Constantinople, and Domnus II, the Patriarch of Antioch, in 448. However, he had been recognized by others as an opponent of Nestorianism, and there were a few who thought that perhaps this condemnation was an attempt to sneak Nestorianism in through the back door. Among these was Dioscorus, Patriarch of Alexandria, who had also attended the Council of Ephesus and had been the secretary of none other than St. Cyril of Alexandria himself. Eutyches, Dioscorus, and others appealed to the Emperor, and the Emperor decided to call another ecumenical council at Ephesus.
The Second Council of Ephesus, which took place in 449, was a bit thrown-together; Pope St. Leo I only had time to put together a brief embassy to represent the West. The Emperor had actually invited him to come and preside over the council himself, but St. Leo declined because he had other things to do, since Italy was being invaded by Attila the Hun. Instead, he sent a bishop, a priest, and a deacon. The bishop, Julius, is otherwise unknown, and seems to have been banished from the council for some reason. The priest, Renatus, died on the way, so only St. Hilarius, the deacon (who would one day become Pope), seems to have represented the West. The honorary ranks were entirely jumbled up. As noted, there seems to have been no episcopal representative of Rome, and St. Hilarius seems to have repeatedly tried in vain to get the council to read St. Leo's letter to it. Dioscorus of Alexandria presided, Juvenal of Jerusalem, an ally of Dioscorus, was treated as next in authority, and Domnus of Antioch and St. Flavian of Constantinople were treated as if their sees were the least important.
Eutyches was brought before the council and affirmed the Nicene Creed, and said that he had been condemned for what was in fact simply an error of phrasing. The council concluded that Eutyches had been wrongly condemned -- quite firmly, for even Domnus of Antioch recanted his condemnation (not that it did him any good, since the council eventually condemned him) -- and voted to depose St. Flavian. It's unclear exactly what went down from this point -- the council itself seems to have tried to convey the impression that it was nearly unanimous, but later claims at Chalcedon were that a great many bishops had begged mercy for St. Flavian and that St. Hilarius, having proclaimed that Rome would reject the decision, only barely escaped with his life. Both are so dramatic in character that it is difficult to say which is the less plausible.
In any case, St. Flavian was sent into exile, and died shortly thereafter. It was actually a pretty thorough victory for Dioscorus and Juvenal -- the Patriarch of Constantinople deposed, the Patriarch of Antioch deposed. According to later claims at Chalcedon, Juvenal decided to add one more and threw together a small synod of bishops at Nicaea to excommunicate the Pope of Rome. Maybe that happened, but it could well just have been a rumor.
St. Flavian had immediately written a letter to St. Leo, although, of course, he died before any answer returned. St. Leo wrote the Emperor and told him he was nullifying all decisions of the council. Famously, he called it a latrocinium, a bandit council, and ever since the Second Council of Ephesus has usually been called the Latrocinium, the Robbers' Synod of Ephesus. In the meantime the Emperor had also died, and a new Emperor took the throne who called a new council to resolve the confusion over the council that had been called to resolve the confusion arising from the synod that had been called to clarify what the Council of Ephesus really meant. It met in late 451 in Chalcedon, near Constantinople. That wasn't the intent. St. Leo had insisted that it should meet in Italy; the Emperor actually summoned the bishops to Nicaea. But the Huns got involved again, since they were invading the East as well as the West, and the council was moved at the last moment to Chalcedon. St. Leo was again asked to preside, but he declined again because it wasn't as if the Huns were on vacation -- that's why he had wanted the council in Italy in the first place. He sent another legation instead.
It was a big council -- the largest of all the first seven ecumenical councils, with over five hundred bishops in attendance from all over the Empire. Dioscorus, however, was refused admittance, and the council deposed him. St. Leo's letter was finally read, and, after some discussion of a few passages that worried some of the Council Fathers as suggesting Nestorianism, was accepted as an accurate statement of orthodoxy, in full conformity with St. Cyril of Alexandria and the Council of Ephesus. In the conciliar definition, they produced the famous Christological formula, "one and the same Christ, Son, Lord, only begotten, to be acknowledged in two natures, without confusion, without change, without division, without separation". They then voted on a series of canonical regulations, although the papal legates were not present for the vote on all of them, leading to the dispute over Canon 28, which gave the see of Constantinople the same honor as the see of Rome.
The Egyptian bishops refused to accept the council, of course, and the schism has never been healed, which is why the Coptic Orthodox are not in communion with either the Catholic or the Eastern Orthodox sees.
In 452, Attila invaded Italy again and conquered the north; he reached the gates of Rome, met St. Leo and two imperial envoys, and after negotiations suddenly went away rather than sack the city. Nobody knows why he left; historians love to speculate, of course, but nobody knows. St. Leo in the meantime, when he wasn't stopping invading armies, was writing letters protesting Canon 28, but in early 453, he affirmed the council on matters of faith (but still not on matters of canonical discipline).
Despite the schism afterward, the Council of Chalcedon was actually in many ways the most orderly ecumenical council in both its proceedings and its aftermath. Given the circumstances, it was doubtful that Alexandria would have ever gone along with any reversal of the Latrocinium, anyway, and for most of the empire it was an easy result to accept.