According to Ludwig Ott, in order for a Council to be Ecumenical or General, three things are necessary: "(1) That all the ruling Bishops in the world be invited; (2) That in point of fact so many Bishops from various countries come, that they may be regarded as being representative of the whole Episcopate; (3) that the Pope summon the Council, or at least invest the assembly with his authority and preside personally or by his representative at the meeting, and ratify the resolutions. From the Papal ratifications, which can be explicit or implicit, the resolutions derive general legal binding power" (Ott, 300).

See also:

• Catholic Encyclopedia article on "Ecumenical Councils"

• Texts for the first Seven Ecumenical Councils

Short Introductions to Each Council:

Nicaea (325)

At the decree of Pope St. Sylvester I and the Emperor Constantine the General Council of Nicaea was convened in 325 AD in order to quell the Arian controversy, which had begun approximately seven years earlier. Arius, a priest from Alexandria, after whom the heresy of "Arianism" is named, taught that the Logos (the Second Person of the Blessed Trinity) is not Divine, but is rather the most perfect and first of God the Father's creatures. Three hundred and eighteen bishops, along with the pope's legates and the emperor, assembled in Nicaea in order to define clearly and forever the Church's doctrine on the Divinity of Christ (the Incarnate Logos) and also to anathematize the Arian heresy. In addition to this chief task of dealing with the Arian heresy, the Council of Nicaea also promulgated many disciplinary canons on a variety of matters. Some of the better known persons who attended and participated at this Council are St. Alexander of Alexandria, St. Eusebius of Nicomedia, St. Athanasius of Alexandria, Eusebius of Caesarea, and Nicholas of Myra. This Council is doctrinally significant for its explicit definition of the Divinity of the Son of God, Who, the Council professes, is of one nature or substance with God the Father. This Council also definitively condemned any theology that holds that the Divine Nature is mutable or subject to change of any sort.
 

Constantinople (381)

This General Council was convened in order to re-condemn the Arian heresy as well as to dogmatically define the Divinity of God the Holy Spirit. The Macedonians, also known as the "Spirit-fighters," held, contrary to traditional Church teaching, that the Holy Spirit was merely a creature and therefore not Divine. It was against this group that the Council's teachings were chiefly directed. In order to make more explicit the Church teaching on the Divinity of the Holy Spirit, the Council Fathers added to the Nicaean creed, after the words "And in the Holy Spirit," the statement "the Lord, the Giver of life, Who proceeds from the Father, Who together with the Father and Son is worshiped and glorified, Who spoke through the prophets." This statement, which clearly and explicitly affirms the Divinity of the Holy Spirit, made it definitively evident that Macedonianism is not within the sphere of orthodox Christianity. Two of the key persons who were involved at the Council of Constantinople are Meletius of Antioch and St. Gregory of Nazianzen.
 

Ephesus (431)

Nestorianism and Pelagianism are the two principal heresies against which the teachings of this General Council were directed. Nestorianism is named after the Bishop of Constantinople, Nestorius, who taught, around the year 430 or so, that in Christ there are two persons, one Divine and one human, which are united morally or accidentally. In other words Nestorius taught that the Divine Son of God and that the human person, Christ, are united to one another in intellect and will by the grace of God. Since Nestorius held that in Christ there were not only two natures but also two persons he then concluded that the Blessed Virgin Mary is not the Mother of God but rather merely the Mother of Christ. Over and against this view the Council Fathers taught that in Christ there is One Person, the Son of God, who has a Divine Nature from all eternity and a human nature from the moment He assumed it at the Incarnation. The Council Fathers also taught that since the Blessed Virgin is the Mother of the Incarnate Word, Who is a Divine Person, She can rightfully be called the Mother of God.

The Pelagian heresy, which St. Augustine fiercely battled during his life, denied Original Sin and maintained that grace is not strictly necessary but rather only morally necessary for salvation. Contrary to Pelagianism the Council Fathers taught that grace is absolutely necessary for man to perform any salutary action whatsoever. Moreover, they maintained that "God thus operates in the hearts of men and in the free will itself, so that a holy thought, a pious plan, and every motion of good will is from God, because we can do anything good through Him, without Whom we can do nothing" (DS, 135).

This Council was presided over by St. Cyril of Alexandria and confirmed by Pope St. Sixtus III.
 

Chalcedon (451)

In the year 451 Pope Leo and the Emperor Marcian assembled one hundred and fifty bishops at Chalcedon. This Fourth Ecumenical Council of the Church was principally convened in order to assert the orthodox Catholic doctrine against the heretical teachings of Eutyches and the Monophysites. Eutyches and the Monophysites taught that in Christ not only is there One Person but there is also only One Nature (i.e., the Divine Nature). These heretics held that when the Word became flesh the human nature was completely and totally absorbed by the Divine Nature such that only One Nature remained. It is interesting to note that the orthodox Christological Doctrine of the Hypostatic Union (i.e., that there are two natures, the Divine and human, joined to each other in the One Divine Person of God the Son), as defined by the Council of Chalcedon, stands as the mean between Nestorianism (two natures and two persons), on the one hand, and Monophysitism (One Nature and One Person), on the other hand. Probably the most famous Christological text from this Council is that which affirms that in Christ there are two natures united "without mingling, without change, indivisibly, undividedly, the distinction of the natures nowhere removed on account of the union but rather the uniqueness of each nature being kept and uniting in One Person and One Substance, not divided or separated into two persons, but one and the same Son only begotten God Word, Lord Jesus Christ" (DS, 148). Unfortunately, this General Council's teachings--concerning the natures of Christ and their relation to one another--were not accepted by all. Many in Egypt, Armenia, Syria and other places refused to accept the definition of Chalcedon. In these locations Monophysites can be found to this day.
 

Constantinople II (553)

This General Council, which was attended by 165 bishops, was held under Pope Vigilius and the Emperor Justinian I. Since there was resistance to the Christological teachings of the Council of Chalcedon the Church decided to call this fifth Ecumenical Council in order to reiterate the teachings of Chalcedon and anathematize various heretics. Some of the better known theologians whose works were condemned at this council are Origen, Theodore of Mopsuestia, Theodoret, and Ibas of Edessa. This General Council also explicitly reaffirmed the dogmatic character of the teachings of the previous four Ecumenical Councils.
 

Constantinople III (680-681)

Called together by Pope Agatho and the Emperor Constantine Pogonatus, the Third General Council of Constantinople was assembled in order to define the Church's position on the two wills of Christ over and against the heresy of Monothelitism. This heresy taught that there was only one will or operation in Christ. Contradicting this heresy, the Council Fathers taught that "similarly we promulgate, according to the teaching of the Holy Fathers, that in Him are also two natural wills and two natural modes of working, unseparated, untransformed, undivided, unmixed; and these two natural wills are not opposed to each other, as the impious heretics maintained." In keeping with the teaching of the Council of Chalcedon this Council strongly emphasized that the doctrine of the "Hypostatic Union" (i.e., that the Divine and human natures in Christ are hypostatically united, that is, joined to each other in One Person).
 

Nicaea II (787)

The Iconoclastic Controversy of the eighth century provided the occasion for the convening of the Second General Council of Nicaea. In 726 the Emperor Leo the Isaurian (717-741), perhaps influenced by Islamic and Jewish attitudes towards images of Christ and the Saints, ordered the destruction of all images in churches. This occasioned a great and bloody schism in the Church and many monks and priests were martyred as they attempted to preserve their sacred icons and statues. Pope Gregory II condemned the Emperor Leo and convoked an Ecumenical Council in 787 in order to deal dogmatically with the problem of iconoclasm. The Council defined that it is permissible and profitable to the faithful to venerate the sacred images of Christ, the Blessed Virgin, the Angels and Saints as well as the relics of the Saints and Martyrs. This Council also condemned the Christological heresy of Adoptionism since this view presupposes Nestorianism, which was already condemned by the Council of Ephesus.
 

Orange II (529)

The Second Council of Orange was not an Ecumenical Council. Nonetheless, due to Pope Boniface II's authoritative confirmation in 531 of this Council's teachings, the Second Council of Orange is held by Roman Catholics to be an infallible rule of the Faith. The main teachings of this Council treat the Doctrines of Original Sin, Grace, and Predestination. In large part these teachings were directed against the Semipelagians. The Semipelagians, while recognizing the reality of original sin and the need for supernatural grace, erred in maintaining that (1) man's natural powers are responsible for his desire for salvation, (2) supernatural grace is not required in order for man to persevere to the end in a state of grace, and (3) by his own natural works man can merit de congruo the first grace. All three of these errors stem from a misunderstanding of the nature of human free will and of the nature of man's cooperation with God's grace.
 

• All conciliar citations are from Henry Denzinger, The Sources of Catholic Dogma.
• The information on the nature of an Ecumenical or General Council is from Ludwig Ott, Fundamentals of Catholic Dogma.