Monophysitism (from the Greek monos meaning 'one' and physis meaning 'nature') is the christological position that Christ has only one nature, as opposed to the Chalcedonian position which holds that Christ has two natures, one divine and one human. There are three major doctrines that can be called monophysite:
Eutychianism holds that the human nature of Christ was essentially obliterated by the Divine, "dissolved like a drop of honey in the sea".
Apollinarism holds that Christ had a human body and human "living principle" but that the Divine Logos had taken the place of the nous, or "thinking principle", analogous but not identical to what might be called a mind in the present day.
Finally, there is the "monophysite" Christology of extant "monophysite" Churches.
However, members of "monophysite" Churches object to the term, preferring the term miaphysite. This term uses a different Greek root, mios meaning 'a complex unity', reflecting their position that in Christ the divine and human nature become one nature, the natures being united without separation, without confusion, and without change.
Later, monothelitism was developed as an attempt to bridge the gap between Monophysitism and the Chalcedonian position, but it too was also rejected by the Chalcedonians, despite at times having the support of the Byzantine Emperors.
Monophysite churches are still found today, and include the Coptic Orthodox Church of Egypt, the Ethiopian Orthodox Tewahedo Church (tewahido being an Ethiopian word meaning "being made one"), the newly autocephalous Eritrean Orthodox Church, and the Armenian Apostolic Church. These are considered branches of Oriental Orthodoxy.