Theologically, to Catholics, the vital distinction is between Eastern Catholic, on the one hand, and schismatics or heretics, on the other.
But it is not convenient to start from this basis in cataloguing Eastern Churches.
To find a time when there was one Eastern Church we must go back to the centuries before the Council of Ephesus (431).
The Latin half was so (in spite of a few unimportant schisms) till the Reformation.
But both these lands eventually fell back into the branches that surrounded them (except for the thin remnant of the Catholic Italo-Greeks).
We may, then, say that any ancient Church east of that line is an Eastern Church.
To these we must add those formed by missionaries (especially Russians) from one of these Churches.
Later Latin and Protestant missions have further complicated the tangled state of the ecclesiastical East.
The Nestorian heresy left a permanent Nestorian Church, the Monophysite and Monothelite quarrels made several more, the reunion with Rome of fractions of every Rite further increased the number, and quite lately the Bulgarian schism has created yet another; indeed it seems as if two more, in Cyprus and Syria, are being formed at the present moment (1908).