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The Arian controversy was a series of Christian disputes about the nature of Christ. It was the greatest internal struggle the Christian Church had so far experienced, and led to the acceptance of the Trinity doctrine, the church’s most fundamental doctrine.
It began in 318 as a dispute between Bishop Alexander of Alexandria and a priest in his diocese named Arius, both Christian theologians from Alexandria, Egypt.
The most important of these controversies concerned the relationship between the substance of God the Father and the substance of His Son. Arius argued that the Son of God did not always exist and that His substance is different from the Father's. This conflicted with the view advanced by Alexander, and later also by Athanasius, who argued that the Christ is coeternal and consubstantial (of the same substance) with God the Father.
Emperor Constantine, through the Council of Nicaea in 325, attempted to unite Christianity and establish a single, imperially approved version of the faith. Ironically, his efforts were the cause of the deep divisions created by the disputes after Nicaea. In the decade after Nicaea, the deposed Arians were readmitted to communion, and all the leading supporters of the Nicene Creed were deposed, disgraced, or exiled.
While there was no formal schism, these disagreements divided the Church into various factions for over 55 years, from the time before the First Council of Nicaea in 325 until after the First Council of Constantinople in 381.
Inside the Roman Empire, the Trinitarian faction ultimately gained the upper hand through the Edict of Thessalonica, issued on 27 February AD 380, which made Nicene Christology the state religion of the Roman Empire, and through strict enforcement of that edict. However, outside the Roman Empire, Arianism and other forms of Unitarianism continued to be preached for some time (without the blessing of the Empire), but it was eventually killed off. The modern Roman Catholic Church and the Eastern Orthodox Church, as well as all Protestant denominations, have generally followed the Trinitarian formulation, though each has its own specific theology on the matter.
General info from Wikipedia.org