Orthodox
Are Catholics and Orthodox still one Church?
Catholics and Orthodox share valid sacraments, apostolic succession, and nearly all doctrine, so the Catholic Church considers Orthodoxy a true 'sister Church' in real, though imperfect, communion — separated canonically since 1054 but united in the essentials of the ancient faith.
Catholic teaching
Vatican II's decree on Ecumenism taught that the Eastern Churches, though not in full communion with Rome, possess true sacraments, especially the Eucharist and priesthood, by which they remain joined to the Catholic Church in a very close, though imperfect, bond, differing chiefly over the exercise of the papacy and the Filioque.
Biblical foundation
Christ's prayer 'that they may all be one' (John 17:21) expresses the Church's deepest identity as visible unity in truth and charity, a unity the Catholic Church holds is substantially preserved with the Orthodox despite the wound of canonical separation.
Scripture references
Historical evidence
In 1965, Pope Paul VI and Ecumenical Patriarch Athenagoras I jointly lifted the mutual excommunications of 1054 in a historic act of reconciliation, and in 2004 the Catholic Church returned relics of St. John Chrysostom and St. Gregory Nazianzen to Constantinople as a gesture of fraternal communion.
The Church Fathers
“What could be more pleasant to hear than that peace and love should be firmly established between the churches?”