Arianism - a heresy of the Early Christian Church relating to definitions of the human or divine status of the person of Jesus Christ, was the first important doctrinal difficulty in the Church after the legalization of Christianity took place under Emperor Constantine I.
Arius was a priest of the Catholic Church in Alexandria, Egypt. In A.D. 321 he was condemned by a synod at Alexandria for teaching a heterodox view of the relationship of Jesus Christ to God the Father. Arius himself died without repudiating his doctrine. Arius and his followers agreed that Jesus was the son of God, but denied that they were one substance. Instead, they viewed God and the Son as being distinct. Jesus is, for Arianism, inferior or subordinate to God the Father.
Because Arius and his followers had great influence in the schools of Alexandria - predecessors of modern universities or seminaries - their theological views spread, especially in the eastern Mediterranean. By 325 the controversy had become significant enough that Emperor Constantine I called an assembly of bishops, the first Ecumenical council at Nicaea, modern Iznik,Turkey (the First Council of Nicaea). The arguments that prevailed at Nicaea were formulated in the Nicene Creed, still recited in Catholic and Orthodox services.
Despite the decision of the Council of Nicaea, Arianism not only survived but flourished for some time. The patronage of members of the imperial family allowed Arian bishops to rule in many centers. Having never converted any sizeable group of the laity, Arianism had died out inside the Empire by the 380s.
However, during the time of Arianism's flowering in Constantinople a missionary named Ulfilas was sent out to the Gothic barbarians across the Danube River. His initial success in converting this Germanic people to an Arian form of Christianity was strengthened by later events. When the Germanic peoples entered the Roman Empire and founded successor-kingdoms, many of them used their Arian religion to differentiate their people from the local inhabitants and maintain their group identity against the Catholic population. See: Ostrogoths, Visigoths, Vandals, Burgundians, Lombards. By the 8th century assimilation had ended any surviving Arian churches. Only the Franks among the Germanic peoples entered the empire as pagans and converted to Catholic Christianity directly.
The modern Jehovahs Witnesses espouse a form of Arianism today, explicitly agreeing with Arius. The Church of Jesus Christ of Latter-day Saints does not explicitly agree, but their belief is very similar. In some ways Jesus is seen as subordinate to God the Father (e.g., he acts on his Father's wishes), but the primary teaching is that as they are both perfect and free from sin, there is no possibility of a disagreement. They are always perfectly aligned and there is no need of establishing a hierarchy.
This, of course, is not to be confused with the Aryans who invaded India long ago.
See also Christology