Today in the Maronite calendar is the memorial for the Fathers of the Holy and Ecumenical Council of Ephesus. The third ecumenical council was as close to being a free-for-all as a council can be.
Nestorius was a monk of Antioch who became famous for the quality of his sermons; because of this, the Emperor Theodosius II named him Patriarch of Constantinople in 428. Almost immediately he found himself dealing with a local dispute between those who claimed that Mary was Theotokos and those who thought it absurd and suggestive of Arianism to say that God had a human mother, because it suggested that the Son began to be. Nestorius proposed and tried to enforce a compromise in which Mary would be called Christotokos and not Theotokos, Christ-bearer rather than God-bearer. The controversy grew, because Nestorius does not seem to have been well liked by the populace, and the news began to spread. The ultimate result was a war of letters between St. Cyril, the Patriarch of Alexandria, and Nestorius. Nestorius was absolutely not prepared for the fight; the strength and influence of Alexandria was immense, and Alexandrians were brawlers, not at all shy about fighting a matter out, and politically cunning, since life in Alexandria required the negotiation of perpetually shifting political alliances.
The great alliance between Rome and Alexandria which largely defines the early conciliar period of the Church had begun to crack in the reign of Cyril's predecessor and uncle, who had leveraged the alliance in a harassment campaign against St. John Chrysostom, but it was not yet broken. Cyril soon wrote to Pope Celestine I of Rome to ask for his decision on the question. Celestine held a synod and came down against Nestorius, authorizing Cyril to speak for Rome in the matter. It was all that Cyril needed to know that he was on sure ground. Constantinople had become increasingly important due to its connection to the Emperor, but against Alexandria and Rome together it was far outmatched.
So Nestorius took what was his only available option: he pushed the Emperor to summon the bishops of the Empire to a council. It is often forgotten that the initiative for the Council of Ephesus was Nestorian -- as far as Cyril was concerned, there could hardly have been any need for a council, since both Rome and Alexandria had spoken on the matter and agreed. It was Nestorius who pressed for a council to exonerate him and condemn Cyril. Nestorius, no doubt, thought that his hand was fairly strong, since he could count on the support of Antioch and the Emperor, and he seems always to have thought that his position was the only reasonable position, rejected by Cyril only because Cyril was obstinate. He was in many ways a thoroughgoing intellectual, fond of 'technically' and 'strictly speaking', and while he seems to have been quite charming personally (people who knew him directly often supported him quite loyally), his entire approach as patriarch was high-handed and condescending.
Theodosius called for a council to open on June 7, 431, in Ephesus. I'm not sure why this city in particular was chosen; perhaps it was intended as a minor concession to the other side, but Ephesus was actively hostile to anything suggestive of Nestorianism, and the bishop of Ephesus, Memnon, would refuse Nestorius entry into all the churches of Ephesus, citing the decisions of Rome and Alexandria. And when Cyril arrived, he took control of everything. The delegations from Rome and Antioch were late because of stormy weather, and Cyril wanted to open on time, but he was told by the imperial representative, Candidian, that it would be illegal to open the council without the reading of the Emperor's convocation letter, and that he should wait until the other delegations arrived. Cyril did wait, for two weeks, and then opened the council, anyway, on June 22, presiding over it as Patriarch of Alexandria and representative of Rome. When Candidian came in with the pro-Nestorian bishops protesting, Cyril had him read the Emperor's letter to the bishops to clarify a point, and then took that reading of the letter as the legal opening of the council.
The council summoned Nestorius, but Nestorius, complaining of harassment by the people of Ephesus, would not recognize any council that was led by Cyril. He refused the summons and was condemned and deposed by the council.
John, Patriarch of Antioch, arrived a few days afterward to find that the council had already started and, in fact, had already condemned Nestorius. Furious, he and Candidian opened a separate council and deposed Cyril and Memnon. Meanwhile, the Roman legation arrived, and, after giving the letters of Pope Celestine to Cyril's council and some brief investigation, they concluded that all that was required was that the documents of the first session be read aloud in their presence. That done, the legates then signed and made Rome's support of the condemnation of Nestorius official.
That in hand, Cyril now began to move against John of Antioch, summoning him to the council. When John refused, he was deposed. Other bishops attempted to take advantage of this -- the bishop of Jerusalem (unsuccessfully) and the bishop of Cyprus (successfully) tried to get the council to recognize its independence form Antioch. Canons were drawn up, and the council came to an end. Throughout the entire period, the Imperial representatives had difficulty keeping order, both sides complained of physical bullying, and the city stayed more or less in uproar mode the entire time.
But its decisions held. Rome confirmed the decisions of the council for the West. Cyril reconciled with John, although only after much negotiation. And the question for the East then became, how strictly should we interpret the decisions of Ephesus? It would take another council a century later to answer that question.