[With Frank's permission, I have added some information here (and in one case changed the order of his contributions) in order to clarify the historical relationship of the views.  My comments are based primarily on William Rusch's historical summary in "The Trinitarian Controversy", Fortress.  I'm going to save this as an FAQ.  --clh]  MAJOR VIEWS OF THE TRINITY   [SECOND CENTURY  The writers of the 2nd Cent. are important, because they set up much of the context for the later discussions.  Justin Martyr, Aristides, Athenagoras, Tatian, and Theophilus of Antioch are known as the "Apologists".  Their theology has often been described as "Logos theology".  Based strongly on wording in John, they took more or less a two-phase approach.  Through eternity, the Logos was with the Father, as his mind or thought.  This "immanent Word" became "expressed" as God revealed himself in history, ultimately in Jesus. Thus Jesus' full distinction from the Father only became visible in history, though the Logos had been present in God from eternity. Rusch regards this view is containing many of the emphases of the final orthodox position, but in a form which is less sophisticated, because it did not have the technical language to properly deal with the eternal plurality in the Godhead.  Irenaeus held views somewhat similar to the Apologists.  However he was uncomfortable with the two-stage approach.  He still viewed God as one personage, with distinctions that did not become fully visible except through his process of self-revelation (the "economy").  The distinctions are present in his essential nature.  Irenaeus emphasized the Holy Spirit more than the Apologists.  Irenaeus' views should probably be called "economic trinitarianism", though that term is normally used (as below) to refer to later developments.   THIRD CENTURY  --clh]  Dynamic Monarchianism   Source: Theodotus Adherents: Paul of Samosota, Artemon, Socinus, Modern Unitarians Perception of God's Essence: The unity of God denotes both oneness of nature and oneness of person. The Son and the Holy Spirit therefore are consubstantial with the Father's divine essence only as impersonal attributes. The divine dunamis came upon the man Jesus, but he was not God in the strict sense of the word. Perception of God's Subsistence: The notion of a subsistent God is a palpable impossibility, since his perfect unity is perfectly indivisible. The 'diversity' of God is apparent and not real, since the Christ event and the work of the Holy Spirit attest only to a dynamic operation within God, not to a hypostatic union. Asignation of Deity/Eternality:  Father: Unique originator of the universe. He is eternal, self-existent, and without beginning or end.  Son: A virtuous (but finite) man in whose life God was dynamically present in a unique way; Christ definitely was not deity though his humanity was deified.  Holy Spirit: An impersonal attribute of the Godhead. No deity or eternality is ascribed to the Holy Spirit. Criticism(s): Elevates reason above the witness of biblical revelation concerning the Trinity. Categorically denies the deity of Christ and of the Holy Spirit, thereby undermining the theological undergirding for the biblical doctrine of salvation. [In summary, this probably best thought of as not being Trinitarianism at all.  God is an undifferentiated one.  Son and Holy Spirit are seen as simply names for the man Jesus and the grace of God active in the Church.  --clh]    Modalistic Monarchianism   Source: Praxeas Adherents: Noatus, Sabellius, Swedenborg, Scleiermacher, United Pentecostals (Jesus Only) Perception of God's Essence: The unity of God is ultra-simplex. He is qualitatively characterized in his essence by one nature and person.  This essence may be designated interchangeably as Father, Son, and Holy Spirit. They are different names for but identical with the unified, simplex God. The three names are the three modes by which God reveals Himself. Perception of God's Subsistence: The concept of a subsistent God is erroneous and confounds the real issue of the phenomenon of God's modalistic manifesting of himself. The paradox of a subsisting "three in oneness" is refuted by recognizing that God is not three persons but one person with three different names and corresponding roles following one another like parts of a drama. Asignation of Deity/Eternality:  Father: Fully God and fully eternal as the primal mode or manifestation of the only unique and unitary God  Son: Full deity/eternality ascribed only in the sense of his being another mode of the one God and identical with his essence. he is the same God manifested in temporal sequence specific to a role (incarnation).  Holy Spirit: Eternal God only as the tile designates the phase in which the one God, in temporal sequence, manifested himself pursuant to the role of regeneration and sanctification. Criticism(s): Depersonalizes the Godhead. To compensate for its Trinitarian deficiencies, this view propounds ideas that are clearly heretical. Its concept of successive manifestations of the Godhead cannot account for such simultaneous appearances of the three persons as at Christ's baptism. [Rusch comments that evidence on these beliefs is sketchy.  There are actually two slightly different groups included: Noetus and his followers, and Sabellius.  Noetus was apparently more extreme. Sabellius followed him, and attempted to use some features of economic Trinitarianism to create a more sophisticated view.  Unfortunately, information about Sabellius comes from a century later, and there seems to be some confusion between him and Marcellus of Ancyra. --clh]   [I've moved the following description to be with the other third-century views.  It originally appeared near the end.  --clh]  "Economic" Trinitarianism   Source: Hippolytus, Tertullian Adherents: Various "neo-economic" Trinitarians Perception of God's Essence: The Godhead is characterized by triunity: Father, Son, and Holy Spirit are the three manifestations of one identical, indivisible substance. The perfect unity and consubstantiality are especially comprehended in such manifest Triadic deeds as creation and redemption. Perception of God's Subsistence: Subsistence within the Godhead is articulated by means of such terms as "distinction" and "distribution" dispelling effectively the notion of separateness or division. Asignation of Deity/Eternality: The equal deity of Father, Son, and Holy Spirit is clearly elucidated in observation of the simultaneous relational/operational features of the Godhead. Co-eternality, at times, does not intelligibly surface in this ambiguous view, but it seems to be a logical implication. Criticism(s): Is more tentative and ambiguous in its treatment of the relational aspect of the Trinity. [Note that this is a development of the Apologists and Irenaeus, as mentioned above.  As with them, the threeness is visible primarily in the various ways that God revealed himself in history.  However they did say that this is a manifestation of a plurality that is somehow present in the Godhead from the beginning.  Tertullian talks of the Father, Son, and Holy Spirit as being three that are one in substance.  Many people regard this view as being essentially orthodox, but with less developed philosophical categories.  --clh]  [Origen, developing further an approach started by Clement, attempted to apply neo-Platonism to Christian thought.  He set many of the terms of the coming battle.  In Platonic fashion, he sees the Son as a mediator, mediating between the absolute One of God and the plurality of creating beings.  The Son is generated, but he is "eternally generated".  That is, the relationship between Father and Son is eternal.  It cannot be said that "there was once when he was not" (a phrase that will haunt the discussion for centuries).  Having the Son is intrinsic to his concept of God.  The Father and Son are described as separate "hypostases", though this may not have quite the meaning of separate subsistence that it had in some contexts.  The union is one of love and action, but there is some reason to think that he may have used the term homoousios ("of the same substance").  The Holy Spirit is also an active, personal substance, originated by the Father through the Son.  Origen's intent is trinitarian, not tritheistic, but he pushes things in the direction of separateness.   FOURTH CENTURY  --clh]  Subordinationism  [often called Arianism --clh]   Source: Arius Major Adherents: Modern Jehovah's Witnesses, and several other lesser known cults Perception of God's Essence: The inherent oneness of God's nature is properly identifiable with the Father only. The Son and the Holy Spirit are discreet entities who do not share the divine essence. Perception of God's Subsistence: The unipersonal essence of God precludes the concept of divine subsistence with a Godhead. "Threeness in oneness" is self- contradictory and violates biblical principles of a monotheistic God. Asignation of Deity/Eternality:  Father: The only one, unbegotten God who is eternal and without beginning.  Son: A created being and therefore not eternal. Though he is to be venerated, he is not of the divine essence.  Holy Spirit: A nonpersonal, noneternal emanation of the Father. He is viewed as an influence, an expression of God.  Deity is not ascribed to him. Criticism(s): It is at variance with abundant scriptural testimony respecting the deity of both Christ and the Holy Spirit. Its hierarchial concept likewise asserts three essentially separate persons with regard to the Father, Christ, and the Holy Spirit. This results in a totally confused soteriology. [Note also that in most versions of this view, the Son is not fully human either.  He is supernatural and sinless.  That distinguishes this view from adoptionism.  --clh]   Orthodox Trinitarianism   Source: Athanasius Adherents: Basil, Gregory of Nyssa, Gregory of Nazianzus, Augustine, Thomas Aquinas, Luther, Calvin, Contemporary orthodox Christianity Perception of God's Essence: God's being is perfectly unified and simplex: of one essence.  This essence of deity is held in common by Father, Son, and Holy Spirit. The three persons are consubstantial, coinherent, co-equal, and co- eternal. Perception of God's Subsistence: The divine subsistence is said to occur in three modes of being or hypostases. As such, the Godhead exists "undivided in divided persons." This view contemplates an identity in nature and cooperation in function without the denial of distinctions of persons in the Godhead. Asignation of Deity/Eternality: In its final distillation, this view unhesitatingly sets forth Father, Son, and Holy Spirit as co-equal and co-eternal in the Godhead with regard to both the divine essence and function. Criticism(s): The only shortcoming has to do with the limitations inherent in human language and thought itself: the impossibility of totally describing the ineffable mystery of "three in oneness." [At least in the 4th Cent, there were several different approaches, all of which fit the description here, and all regarded as orthodox, but which are somewhat different in detail.  Nicea was originally held to respond to Arius.  Arius can be thought of as carrying Origen's thought a bit too far, to the point of making the Son a separate entity.  In general the East tended to take an approach based on Origen's, and it was hard to get acceptance of Nicea in the East.  Its final acceptance was based on the work of Athanasius with the Cappadocians: Gregory of Nyssa and Gregory of Nazianzus, among others.  While starting with three, they show that their unity in nature and and action is such that one must think of them as being a single God.  This allowed the Council of Constantinople, in 381, to get wide agreement on the idea of three hypostatese and one ousia.  --clh]  Adapted from _Charts of Christian Theology and Doctrine_, by H. Wayne House.   Frank