Monarchianism is a set of beliefs that emphasize God as being one person, in direct contrast to Trinitarianism which defines God as three persons coexisting consubstantially as one in being. The term was given to Christians who upheld the full divinity of Christ against the Arians, Subordinationists and Adoptionists.
Various models of resolving the relationship between the God the Father and the God the Son were proposed in the 2nd century, but later rejected in favor of the doctrine of the Trinity as expounded at the First Council of Constantinople. It was decided that God was one being who consisted of three persons: the Father, the Son, and the Holy Spirit.
Two contradictory models of monarchianism have been propounded:
- Modalism (or modalistic monarchianism) considers God to be one person appearing and working in the different "modes" of the Father, the Son, and the Holy Spirit. The chief proponent of modalism was Sabellius, hence the view is commonly called Sabellianism. It has also been rhetorically labeled Patripassianism by its opponents, because according to them it purports that the Person of God the Heavenly Father suffered on the cross.
- Dynamic monarchianism holds that God is one being, above all else, wholly indivisible, and of one nature. It reconciles the "problem" of the Trinity (or at least Jesus) by holding that the Son was not co-eternal with the Father, and that Jesus Christ was essentially granted godhood (adopted) for the plans of God and for his own perfect life and works. Different variations of Dynamism hold that Jesus was "adopted" either at the time of his baptism or his ascension. An early exponent of this belief was Theodotus of Byzantium.
Both schools of Monarchians found a strong wall of opposition to them elevated very quickly in the form of the Logos theologians (Tertullian, Hippolytus, Clement of Alexandria, and Origen of Alexandria).
The name Monarchian properly does not stricly apply to the Adoptionists, or Dynamists, as they "did not start from the monarchy of God, and their [doctrine] is strictly Christological". 
See also 
- Encyclopaedia Britannica: Monarchianism
- Monarchians at Catholic Encyclopedia, newadvent.org
- Oxford Dictionary of the Christian Church (Oxford University Press 2005 ISBN 978-0-19-280290-3): Monarchianism
- Knight, Kevin (ed.), "The dogma of the Trinity", Catholic Encyclopedia, New Advent
- The SCM Press A-Z of Patristic Theology, entry Monarchianism, p. 227
- Catholic Encyclopedia - Monarchians