From the fourth to the eighth century tension already existed in the Church between East and West over the true significance of the Roman primacy. (...) The latent tension only came to the surface in the ninth century, when it developed into open hostility.
The political event which occasioned this conflict was the founding of the Carolingian Empire in the West.
(...) When a project for the marriage of Charles and the reigning Byzantine empress fell through, the Frankish king decided to ruin Constantinople's claim to universal jurisdiction. One of the means used to achieve this end was to bring the charge of heresy against the East. The Eastern emperor could not claim to be the successor of earlier Christian basileis because he worshipped images and because he confessed that the Holy Spirit proceeds "from the Father by the Son" instead of "from the Father and the Son." These allegations by Charlemagne in his famous Libri Carolini, sent to the pope in 792, formed part of the Frankish refutation of the decrees of the Second Ecumenical Council in Nicaea (787) and prepared the way for the interminable quarrel between East and West over the question of the Filioque. [During the sixth century certain anti-Arian councils in Spain had inserted in the Nicaean-Constantinopolitan Creed the word Filioque which was not in the original (Credo ... in Spiritum Sanctum ...qui ex Patre Filioque procedit).
This new version of the Creed spread to Gaul and the Frankish lands in the eighth century. It was not accepted by the Church of Rome, which opposed the interpolation until the eleventh century.]
(...)Fortunately for the cause of church unity, while the Roman Church approved Charlemagne's political aims, it was decidedly opposed to his theological attack on Byzantium. Popes Hadrian I (772-795) and Leo III (795-816) defended the Council of Nicaea and formally rejected the interpolation in the Creed. (pp. 41-43)
...The way in which the Fathers interpret the transcendence of God; that is, God remains unknowable in his unique essence, but he has revealed himself as a Trinity of Three Persons. The God of the Bible therefore in known to the extent that He is a living and acting Deity, the One who has sent His Son for the salvation of the world. This particular emphasis of the thought of the Eastern Fathers distinguishes them - (...) - to the way in which their Latin brothers preferred to think of God first as a unique essence, and then only as a Trinity. These two different attitudes would later give rise to two schools of Trinitarian theology. In Latin theology, the divine Persons were considered as the simple inner relations of the unique essence of the Godhead: hence, if the very existence of the Spirit is determined by its relations to the Father and the Son, the doctrine of the Filioque - or procession of the Spirit from the Father and the Son - becomes a logical, dogmatic necessity, for the Spirit cannot be said to be distinct from the Son if he does not proceed from him. Eastern theologians, on the other hand, remained faithful to the old "personalism" of the Greek Fathers. The doctrine of the Filioque appeared to them, consequently, as Semi-Sabellianism (to use the expression of Photius). [Sabellianism is a heresy dating from the second century attributed to a certain Sabellius, who taught that the divine Persons are simply "modes" or "aspects" of a unique God.] Consubstantial with the Father and the Son, because proceeding from the Father, the unique source of the Deity, the Spirit has his own existence and personal function in the inner life of God and the economy of salvation: his task is to bring about the unity of the human race in the Body of Christ, but he also imparts to this unity a personal, and hence diversified, character. It is with a prayer to the Holy Spirit that all the liturgical services of the Orthodox Church begin, and with an invocation of his name that the eucharistic mystery is effected. (pp. 195-197)