The infelicitous term Oriental Orthodoxy refers to several particularly ancient Orthodox Christian traditions. The Oriental Orthodox churches separated from the then-still-unified vast communion that called itself the One Holy Catholic and Apostolic Church in the 5th century, centuries before the 11th-century Great Schism in which that larger church separated into the "Western Church" (Roman Catholicism) and the Eastern Orthodox Church. (The term is infelicitous because oriental as a common adjective means the same thing as eastern, and yet Oriental Orthodoxy is not the same thing as Eastern Orthodoxy.)
The separation resulted in part from the Oriental Orthodox churches' refusal to accept the Christological dogmas promulgated by the Council of Chalcedon, which held that Jesus has two natures -- one divine and one human. The Oriental Orthodox churches are therefore often called Monophysite churches, although they reject this label, prefering the term "non-Chalcedonian" or "Miaphysite" churches.
Oriental Orthodox churches include:
The Assyrian Church of the East is sometimes considered an Oriental Orthodox Church, although they left the Catholic and Apostolic Church before the Council of Chalcedon and revere Saints anathemized by the previously mentioned Churches. In addition, they accept Christology that is rejected by the Oriental Orthodox Communion.