Constantine convened bishops from across the empire at Nicaea in 325. The council produced a creed declaring the Son homoousios with the Father, of one substance, co-eternal and uncreated, directly rejecting Arius's teaching, and Arius himself was exiled. The condemnation did not end the argument. Constantine later readmitted Arius to communion under pressure from his Eastern allies, and for the better part of the fourth century the empire's bishops split repeatedly over rival creeds, exiles and reinstatements that tracked the shifting sympathies of successive emperors rather than a settled theological consensus. Arius died in Constantinople in 336, and the wider controversy that carried his name was not closed until the First Council of Constantinople in 381 reaffirmed and extended the Nicene formula.
Arian Christianity did not simply disappear with that ruling. Ulfilas, a fourth century Gothic bishop trained in the Eastern church during the years Arian theology held real influence there, translated scripture into Gothic and evangelized the Goths in a non-Nicene form of Christianity that spread with them into the Vandal, Lombard and Visigothic kingdoms, persisting in parts of Western Europe for two more centuries after Nicaea and Constantinople had settled the question for the imperial church.
Modern scholarship treats the label "Arianism" with some caution. Because Arius's own writings survive only as fragments embedded in hostile sources, and because later figures such as Eunomius pushed subordinationist Christology further than Arius himself is known to have gone, historians debate how far the developed "Arian" theology of the following decades should be read back onto Arius the man rather than onto a movement that grew past him.