Omophorion

In the Eastern Orthodox and Eastern Catholic liturgical tradition, the omophorion (, meaning "[something] borne on the shoulders"; Slavonic: омофоръ, "omofor") is the distinguishing vestment of a bishop and the symbol of his spiritual and ecclesiastical authority. Originally woven of wool, it is a band of brocade decorated with four crosses and an eight-pointed star; it is worn about the neck and shoulders. 
By symbolizing the lost sheep that is found and carried on the Good Shepherd's shoulders, it signifies the bishop's pastoral role as the icon of Christ. All Orthodox bishops wear the "omophorion." Clergy and ecclesiastical institutions, including seminaries, subject to a bishop's authority are often said to be "under his "omophorion"".
The equivalent vestment in Western Christian usage is the archiepiscopal "pallium," the use of which is subject to different rubrics and restrictions. 
Use.
The "omophorion" has two forms: the ancient great "omophorion", which passes around the neck, is folded in the front, and hangs down past the knees in both the front and the back, like a loosely worn long scarf; and the small "omophorion" which is much simpler, passing around the neck and hanging down in the front similar to an "epitrachelion" (stole), only wider and shorter, coming down a little past the waist. Because of the complexity of the great "omophorion", and because of the dignity of the episcopal office, whenever the bishop puts on the "omophorion" or takes it off, he is assisted by two subdeacons.
Whenever the bishop presides at any divine service, he will be vested in the "omophorion". If he is serving the Divine Liturgy, he will wear both the great and the small "omophorion" at different times over his liturgical vestments. At any service other than the Divine Liturgy, he will usually wear the small "omophorion".
At the Divine Liturgy, the rubrics call for the bishop to put on and take off the "omophorion" numerous times. When he is first vested, the subdeacons place the great "omophorion" on him, but afterwards, when the rubric calls for him to wear the "omophorion", it is replaced, for the sake of convenience, with the small "omophorion". 
In modern practice in the Slavic tradition, when several bishops concelebrate, it is now the custom for the chief celebrant to use the great "omophorion" when called for, and the other bishops to wear the small "omophorion" throughout, with all bishops wearing their mitres. In modern Greek Patriarchal practice, on the other hand, all concelebrating bishops wear the great omophorion at the beginning of the Divine Liturgy, with only the chief celebrant wearing the mitre and the other bishops wearing their kalimavkia with the Epanokalimavkion. In other local Churches, notably the Church of Greece, all concelebrating bishops wear both the great omophorion and the mitre, and even carry their staffs.
In the Ruthenian Catholic Church and the Ukrainian Greek Catholic Church, often only the great "omophorion" is used. In this simplified usage, the great "omophorion" is not replaced by the small "omophorion", and is worn by the bishop throughout the entire liturgy. In such cases, the "omophorion" is often sewn into shape and can be simply draped onto the shoulders rather than wrapped on by assistants. Some Ukrainian Greek Catholic bishops, however, insist on the full ceremonial.
During the All-Night Vigil, the bishop will wear the small "omophorion" at the beginning, but near the end will change into the great "omophorion" for the Great Doxology.
Development.
In the early church, the "omophorion" was a broad band of white wool ornamented with crosses and draped loosely over the neck, shoulders, and breast. The modern Roman "pallium" developed from this early "omophorion." In the West, over the centuries, its form has changed into a circular, thin woolen garment for the shoulders, with short, weighted pendants before and behind. The papal "pallium," originally adopted by Pope Benedict XVI at the beginning of his pontificate, is closer to the original "omophorion". Pope Benedict XVI later reverted to the original design of the "pallium", but with red crosses instead of black.
In the East, the only change in the "omophorion" has been an increase in its width and a shift in the material from which it is made. The "omophorion" was documented about the year 400 AD as a liturgical vestment of the bishop in Isidore of Pelusium. It was made of wool and was already seen as symbolic of the duties of bishops as shepherds of their flocks. In the miniatures of an Alexandrian "Chronicle of the World", written probably during the fifth century, the "omophorion" was represented in an image. In later times, it was shown on the renowned ivory tablet of Trier, depicting the solemn translation of relics. Among the pictures dating from the seventh and eighth centuries, in which the "omophorion" is illustrated, are the lately discovered frescoes in "S. Maria, Antiqua" in the Roman Forum. The representation of the "omophorion" in these frescoes is essentially the same as the vestment in its present form.
The "omophorion" probably developed from the civil "omophorion", a shoulder garment or shawl in general use. Bishops may have introduced directly by a positive precept a humeral cloth resembling the ordinary "omophorion" and called by that name, to be used as a liturgical pontifical badge. Alternatively, bishops may have used the civil "omophorion" as an ornament without any special significance, but in the course of time it gradually developed associations as a distinctively episcopal ornament. Finally it symbolized an episcopal badge of office.
Oriental Orthodoxy.
In Oriental Orthodoxy, the "omophorion" takes a number of different forms: