Watson's Biblical & Theological Dictionary 
this ancient sect, was unquestionably so called from Arius, a presbyter of Alexandria, in the early part of the fourth century. It is said that he aspired to episcopal honours; and after the death of Achilles, in A.D. 313, felt not a little chagrined that Alexander should be preferred before him. Whether this circumstance had any influence on his opinions, it is impossible to say; but one day, when his rival (Alexander) had been addressing the clergy in favour of the orthodox doctrine, and maintaining, in strong and pointed language, "that the Son of God was co-eternal, co- essential, and co-equal with the Father," Arius considered this as a species of Sabellianism, and ventured to say, that it was inconsistent and impossible, since the Father, who begat, must be before the Son, who was begotten: the latter, therefore, could not be absolutely eternal. Alexander at first admonished Arius, and endeavoured to convince him of his error; but without effect, except that he became the more bold in contradiction. Some of the clergy thought their bishop too forbearing, and it is possible he felt his inferiority of talent; for Arius was a man of accomplished learning, and commanding eloquence; venerable in person, and fascinating in address. At length Alexander was roused, and attempted to silence Arius by his authority; but this not succeeding, as the latter was bold and pertinacious, Alexander, about the year 320, called a council of his clergy, by whom the reputed heretic was deposed and excommunicated. Arius now retired into Palestine, where his talents and address soon made a number of converts; and among the rest, the celebrated Eusebius, bishop of Nicomedia, and other bishops and clergy of those parts, who assembled in council, and received the excommunicated presbyter into their communion. Eusebius also, having great interest with Constantia, the sister of Constantine, and wife of Licinius, recommended Arius to her protection and patronage; through which, and by his own eloquent letters to the clergy in various parts, his system spread with great rapidity, and to a vast extent. The emperor Constantine, who had no great skill in these matters, was grieved to see the Christian church (but just escaped from the red dragon of persecution) thus torn by intestine animosity and dissensions; he therefore determined to summon a general council of the clergy, which met at Nice, A.D. 325, and contained more than 300 bishops. Constantine attended in person, and strongly recommended peace and unanimity. Athanasius was the chief opponent of the Arians. Both parties were willing to subscribe to the language of the Scriptures, but each insisted on interpreting for themselves. "Did the Trinitarians," says Mr. Milner, "assert that Christ was God? The Arians allowed it, but in the same sense as holy men and angels are styled gods in Scripture. Did they affirm that he was truly God? The others allowed that he was made so by God. Did they affirm that the Son was naturally of God? It was granted: Even we, said they, are of God, ‘of whom are all things.'" At length the Athanasians collected a number of texts, which they conceived amounted to full proof of the Son being of one and the same substance with the Father; the Arians admitted he was of like substance, the difference in the Greek phrases being only in a single letter,—ομοουσιος , homoousios, and ομοιουσιος , homoiousios. At length the former was decreed to be the orthodox faith, and the Nicene creed was framed as it remains at this day so far as concerns the person of the Son of God, who is said to be "begotten of his Father before all worlds; God of God, Light of Light, very God of very God, begotten, not made, of one substance with the Father, by whom all things were made," &c.
Arius was now excommunicated. The sentence of the council pronounced against him and his associates was followed by another of the emperor, whereby the excommunicated persons were condemned to banishment, that they might be debarred the society of their countrymen whom the church had judged unworthy to remain in her communion. Soon after which, Eusebius of Nicomedia, and Theognis of Nice, being found to continue their countenance and protection to the Arian cause, to communicate with those whom they had anathematized, and to concur in those sentiments which they had condemned by their subscriptions; they were both subjected to the same penalty of exile by the emperor, and were actually deposed, (as we learn from Athanasius,) and had successors ordained to their sees, though history is silent as to the council by which this was done. But such was the good nature and credulity of Constantine, that these men, by their usual artifices, easily imposed upon him, and brought him to such a full persuasion of their agreement with the Nicene faith, that in about three years' time they were not only recalled from banishment, but restored to their sees, and to a considerable degree of interest at court. Their thorough attachment to the cause of Arius, and their hatred of Athanasius, who had so vigorously withstood them in the council, and was now advanced to the see of Alexandria, made them watchful of every opportunity to defeat the decisions of the council.
In the meantime one who wished well to their designs, and whom Constantia had upon her death bed recommended to the emperor, did so far prevail upon the easy credulity of Constantine, by complaining that Arius had been misrepresented, and differed nothing in his sentiments from the Nicene fathers, that the indulgent emperor recalled him from his banishment, and required him to exhibit in writing, a confession of his faith. He did this in such terms as, though they admitted of a latent reservation, yet bore the appearance of being entirely catholic; and therefore not only gave satisfaction to the emperor, but even offended some of his own followers, who from that time forth separated from him. The discerning Athanasius was not so easily imposed upon as Constantine; but, well assured of the heretic's prevarication, was resolute in refusing to admit him to communion, whom the Nicene council had so openly condemned. Upon this the emperor sent for Arius to Constantinople, and insisted upon his being received into communion, by Alexander, bishop of that city.
However, on the day before this was to have taken place, Arius died suddenly from a complaint in his bowels. Some attributed this to poison; others to the judgment of God. The emperor did not long survive; and Constantius, his successor, became warmly attached to the Arian cause, as were all the court party. Successive emperors took different sides, and thus was the peace of the church agitated for many years, and practical religion sacrificed alternately to the dogmas or the interests of one party or the other; and each was in turn excommunicated, fined, imprisoned, or banished. Constantius supported Arianism triumphantly. Julian laughed at both parties, but persecuted neither. Jovian supported the Nicene doctrine. Valentinian, and his brother Valens, took contrary sides; the former supporting Athanasianism in the west, and the latter Arianism in the east; so that what was orthodoxy at Rome was heresy at Constantinople, and vice versa. The Arians themselves were not unanimous, but divided into various shades of sentiment, under their respective leaders; as Eusebians, Eudoxians, Acasians, Aetians, &c; but the more general distinction was into Arians and Semi-Arians; the former sinking the character of the Son of God into that of a mere creature, while the latter admitted every thing but the homoousian doctrine, or his absolute equality with the Father. After this period we hear little of Arianism, till it was revived in England in the beginning of the last century by the eccentric Mr. Whiston, by Mr. Emlyn, and Dr. Samuel Clarke. The latter was what may be called a high or Semi- Arian, who came within a shade of orthodoxy; the two former were low Arians, reducing the rank of our Saviour to the scale of angelic beings—a creature "made out of nothing." Since this time, however, both Arians and Socinians are sunk into the common appellation of Unitarians, or rather Humanitarians, who believe our Saviour (as Dr. Priestley expresses it) to be "a man like themselves. The last advocates of the pure Arian doctrine, of any celebrity, were Mr. Henry Taylor, (under the signature of Ben Mordecai,) and Dr. Richard Price, in his "Sermons on the Christian Doctrine." It may be proper to observe, that the Arians, though they denied the absolute eternity of the Son, strongly contended for his pre-existence, as the Logos, or the Word of God, "by whom the worlds were made;" and admitted, more or less explicitly, the sacrifice which he offered for sin upon the cross.
Charles Buck Theological Dictionary 
Followers of Arius, a presbyter of the church of Alexandria, about 315, who maintained that the Son of God was totally and essentially distinct from the Father; that he was the first and noblest of those beings whom God had created
the instrument, by whose subordinate operation he formed the universe; and therefore, inferior to the Father both in nature and dignity: also that the Holy Ghost was not God, but created by the power of the Son. The Arians owned that the Son was the Word; but denied that word to have been eternal. They held that Christ had nothing of man in him but the flesh, to which the word, was joined, which was the same as the soul in us.
The Arians were first condemned and anathematised by a council at Alexandria, in 320, under Alexander, bishop of that city, who accused Arius of impiety, and caused him to be expelled from the communion of the church; and afterwards by 380 fathers in the general council of Nice, assembled by Constantine, in 325. His doctrine, however, was not extinguished; on the contrary, it became the reigning religion, especially in the East. Arius was recalled from banishment by Constantine in two or three years after the council of Nice, and the laws that had been enacted against him were repealed. Notwithstanding this, Athanasius, then bishop of Alexandria, refused to admit him and his followers to communion.
This so enraged them, that, by their interest at court, they procured that prelate to be deposed and banished; but the church of Alexandria still refusing to admit Arius into their communion, the emperor sent for him to Constantinople; where upon delivering in a fresh confession of his faith in terms less offensive, the emperor commanded him to be received into their communion; but that very evening, it is said, Arius died as his friends were conducting him in triumph to the great church of Constantinople. Arius, pressed by a natural want, stepped aside, but expired on the spot, his bowels gushing out. The Arian party, however, found a protector in Constantius, who succeeded his father in the East. They underwent various revolutions and persecutions under succeeding emperors; till, at length, Theodosius the Great exerted every effort to suppress them. Their doctrine was carried, in the fifth century, into Africa, under the Candals; and into Asia under the Goths.
Italy, Gaul and Spain, were also deeply infected with it; and towards the commencement of the sixth century, it was triumphant in many parts of Asia, Africa, and Europe; but it sunk almost at once when the Vandals were driven out of Africa, and the Goths out of Italy, by the arms of Justinian. However, it revived again in Italy, under the protection of the Lombards, in the seventh century, and was not extinguished till about the end of the eighth. Arianism was again revived in the West by Servetus, in 1531, for which he suffered death. After this the doctrine got footing in Geneva, and in Poland; but at length degenerated in a great measure into Socinianism. Erasmus, it is thought, aimed at reviving it, in his commentaries on the New Testament: and the learned Grotius seems to lean that way. Mr. Whiston was one of the first divines who revived this controversy in the eighteenth century. He was followed by Dr. Clarke, who was chiefly opposed by Dr. Waterland.
Those who hold the doctrine which is usually called Low Arianism, say that Christ pre-existed; but not as the eternal Logos of the Father, or as the being by whom he made the worlds, and had intercourse with the patriarchs, or as having any certain rank or employment whatever in the divine dispensations. In modern times, the term Arian is indiscriminately applied to those who consider Jesus simply subordinate to the Father. Some of them believe Christ to have been the creator of the world; but they all maintain that he existed previously to his incarnation, though in his pre-existent state they assign him different degrees of dignity. Hence the terms High and Low Arian.
See PRE-EXISTENCE. Some of the more recent vindicators of Arianism have been H. Taylor in his Apology of Ben Mordecai to his Friends for embracing Christianity; Dr Harwood, in his Five Dissertations; Dr. Price, in his Sermons on the Christian Doctrine.
See also the 4th vol. of the Theological Repository, p. 153-163, and Cornish's Tract on the Pre-existence of Christ. On the opposite side, Bogue and Bennett's Hist of Dissenters, vol. 3: Abbadie, Waterland, Guyse, Hey, Robinson, Eveleigh, Hawker on the Divinity of Christ;
Calamy, Taylor, Gill, Jones, Pike, and Simpson, on the Trinity.