Chalcedon settled Christology for the churches that received it and split the church for those that did not. The bishops of Egypt, of much of Syria and later of Armenia and Ethiopia held that the definition's language of two natures conceded too much to Nestorius and betrayed Cyril of Alexandria, whose formula of one incarnate nature of the Word they regarded as the standard of orthodoxy. The churches descending from that refusal are the Oriental Orthodox, and their separate existence dates from this council.
Calling that position monophysite, which older Western writing routinely did, misstates it. Eutyches taught that the humanity was swallowed by the divinity, and the Oriental Orthodox condemned him too. Their position, generally called miaphysite, holds one united nature in which the divine and the human remain complete and unmixed. The distinction is not a technicality: the whole dispute is about whether that formula and the Chalcedonian one describe the same faith in different vocabularies.
Modern dialogue has moved a long way on precisely that question. Bilateral agreed statements between Oriental Orthodox and both Eastern Orthodox and Catholic churches have declared that the parties confess the same faith in Christ, while the canonical separation continues and the anathemas of 451 remain part of the record. Fifteen hundred years of divergent liturgy, hierarchy and law are not undone by agreeing about a formula, which is itself a fact worth knowing about how churches divide.