There were three ecumenical church councils that took place in Constantinople. To be an ecumenical council meant that representatives from all of the branches of the Christian church (both East and West) met and acknowledged the rulings of the councils as authoritative for the life of the church. The three Councils of Constantinople took place in 381, 553, and 681.
What makes this confusing is that the First Council of Constantinople (381) was the Second Ecumenical Council of the church; the Second Council of Constantinople (553) was the Fifth Ecumenical Council of the church; and the Third Council of Constantinople (681) was the Sixth Ecumenical Council.
The First Council of Constantinople (381) marked the final ruling in the Arian controversy. The Arians had argued that the Son was a lesser degree of deity than the Father, while orthodox theologians like Athanasius insisted that each of the Persons of the Trinity was fully and equally God. Though the Council of Nicaea had previously developed the first draft of the famous Nicene Creed, it was not until the First Council of Constantinople that the formula of God as three co-equal Persons was formally approved by the church. So, at Constantinople in 381, Nicaea was reaffirmed and Arianism was finally and officially banned from the church.
The Second Council of Constantinople (553) shifted from the Trinitarian controversy to issues of Christology. In 451, the famous Council of Chalcedon affirmed that Jesus Christ was fully God and fully man—two natures in one Person—and thereby condemned Nestorianism and Eutycheanism. Over 100 years later, in 553, the Second Council of Constantinople revisited the issue of Nestorianism. There were still a significant number of people in the church who leaned towards Monophysitism, the belief that there was only one nature in Christ. Because of this, they were very much opposed to Nestorianism. The Emperor Justinian hoped to reconcile these Monophysites by making clear to them his complete dismissal of Nestorianism. So, at this council, the writings of several theologians, such as Theodore of Mopsuestia, were condemned (perhaps wrongly) as Nestorian.
The church was (and is) facing theological dangers, and faithful theologians met time after time to examine Scripture and construct coherent responses to heretical theology.
During the century after the Second Council of Constantinople, a variety of the Monophysite heresy sprang up again. With the church taking such a strong position against Nestorianism, many were inclined to lean in the opposite direction. Consequently, a belief called Monothelitism was prevalent. It asserted that there was only one divine will in Christ. The Third Council of Constantinople (681) ruled Monothelitism heretical and instead affirmed Diothelitism, which said that Christ had both a human and a divine will, while maintaining that there was only one Person in Christ.
The Councils of Constantinople are not the “big name” church councils (such as Nicaea and Chalcedon). However, the church was (and is) facing theological dangers, and faithful theologians met time after time to examine Scripture and construct coherent responses to heretical theology. The church is “to contend for the faith that was once for all delivered to the saints” (Jude 3), and the Councils of Constantinople are perfect illustrations of it doing just that.