Broadly speaking, trinitarian theology is any Christian theology that accepts the doctrine that God is "triune," or three beings in one. The Father, the Son, and the Holy Spirit, according to trinitarian theology, are three separate, eternal beings, but one in nature. This doctrine has roots in very early church history, but does not have universal acceptance among Christians. "Trinitarian Theology" may also refer specifically to movements beginning in the 20th century that view the doctrine of the Trinity as the core doctrine of Christian belief and practice.
The doctrine of the Trinity was systematized at the First Council of Nicaea in A.D. 325 as an attempt to deal with varying doctrines regarding the relationship between Jesus and God. The most prominent of these doctrines was Arianism, which asserted that Jesus was something in between human and divine, but not sharing in God's divine nature. One key result of the first Council of Nicaea was what has become known as the Nicaean Creed, which affirms the divinity and unity of all three persons of the Trinity and is recited as part of the liturgy of many Christian worship services.
Although trinitarianism has historically been the dominant viewpoint of the major branches of Christianity, many theological traditions reject it for one reason or another. The most common criticism leveled against trinitarian theology is that it is not strictly monotheistic, meaning that it is a logical contradiction to say that there is one God, while also saying that God is three persons. Trinitarians, however, respond that the claim that the three persons constitute one being makes their doctrine monotheistic.
Trinitarian theology is also criticized by some, especially conservative evangelicals, for being non-biblical either in its terminology or in its conclusions. No word used in either the Old Testament or the New Testament can be translated "Trinity," nor does the Bible teach explicitly about the personhood of the members of the Trinity. Conservatives may argue that the use of non-biblical terms will necessarily lead to non-biblical doctrine, but trinitarians believe there is sufficient scriptural support to justify them using the terms anyway.
A number of alternative theories have been proposed to deal with the perceived weaknesses of trinitarian theology. For instance, Unitarian theology asserts that Jesus was a prophet and maybe a supernatural being of some sort, but not God. Oneness Pentecostals, on the other hand, argue that the Father, Son, and Holy Spirit are not three separate persons, but rather three different roles played by the same person.
The term "Trinitarian Theology," often capitalized when used in this sense, may also reference the view that trinitarian doctrine cannot be separated from any other Christian belief. Theologians and movements that hold to this view see the Trinity as the means by which God came to earth, and therefore the means by which humans are saved. One such movement is the Grace Communion International Church.