The council was called by the Emperor Theodosius the Younger, who had previously called the First Council of Ephesus in 431 AD.
It was called to deal with the controversy surrounding what appeared to be a resurgence of Theodoreanism in the East. Ibas had been producing Syriac translations of Theodore's works, Theodoret had been confined to his See as having a doubtful Orthodoxy, Nestorius' fellow exile Irenaeus had made his way back to the East and become the bishop of Tyre. The final straw came when Eutyches, a fairly well-known Archimandrite of Constantinople, was condemned by the Home Synod of Constantinople as an Apollinarian. The language used in the prosecution would have condemned St Cyril himself and was a clear challenge to the unsteady settlement of 433 AD which was already breaking down. Of course the agreement of 433 AD was never more than a sticking plaster since both sides understood that the other had capitulated, while of course neither had done.
At Ephesus II the first issue was dealing with the condemnation of Eutyches, and in consequence the position of Eusebius and Flavian. I have written about Eutyches and those aspects of Ephesus II relevant to his case here http://www.britishorthodox.org/117m.php
The second session dealt with the following cases - all generally associated with the resurgence of Theodoreanism.
1. Ibas, bishop of Edessa - very important and detailed depositions. He was well known as an active supporter of Theodore and an opponent of St Cyril of Alexandria, and had written the Letter to Maris which was presented here.
2. Daniel of Charrae - he was Ibas' nephew, and had already admitted to adultery and other moral defects and had presented a resignation in a previous enquiry so that there would be no scandal before the pagans. The case had been remitted to the ecumenical council.
3. Irenaeus of Tyre - He had been exiled with Nestorius but returned and was consecrated a bishop by Theodoret. He had already been the subject of an imperial order in 448AD ordering him not to dress as or call himself a bishop.
4. Aquilinus of Byblus - He had been consecrated by Irenaeus of Tyre. He had constantly refused to condemn Nestorius.
5. Sophronius of Constantia - He was also a nephew of Ibas. He was accused by local clergy and monks of praticing astrology. His case was reserved to whoever would be consecrated bishop of Edessa in place of Ibas - since Sophronius was a suffragan.
6. Theodoret - Another major case. Modern scholarship concurs with the view of the council that he never changed from his pre-Ephesine Christology, which was essentially Theodorean. Among the evidence presented against him was a book he had written - An Apology of Theodoret, Bishop, on behalf of Diodore and Theodore, Warriors for the True Religion.
[Domnus of Antioch] - He has been ill and absent from the proceedings but sends a note saying that he approves of all that has taken place.
7. Domnus of Antioch - He was a friend of Theodoret and allowed him to preach in his own Church, and failed to take any action against Ibas. He had not condemned Irenaeus. He professed himself unable to accept the 12 Chapters of St Cyril because his bishops and clergy would all abandon him if he did.
There then follows a decree of the Emperor Theodosius confirming the authority of the ecumencal council.
I hope this brief outline helps a little.