According to the Bible, Nimrod was the son of Cush and grandson of Ham; his name has become proverbial as that of a mighty hunter. His "kingdom" comprised Babel, Erech, Accad, and Calneh, in the land of Sinar, otherwise known as the land of Nimrod.  He plays a signifigant role in rabbinic literature.
Nimrod in Rabbinic Literature
Nimrod is considered the prototype of a rebellious people, his name being interpreted as "he who made all the people rebellious against God" He is identified with Cush and with Amraphel, the name of the latter being interpreted as "he whose words are dark". As he was the first hunter he was consequently the first who introduced the eating of meat by man. He was also the first to make war on other peoples.
His Feats as a Hunter
Nimrod was not wicked in his youth. On the contrary, when a young man he used to sacrifice to God the animals which he caught while hunting. His great success in hunting was because he wore the coats of skin which God made for Adam and Eve. These coats were handed down from father to son, and thus came into the possession of Noah, who took them with him into the ark, whence they were stolen by Ham. The latter gave them to his son Cush, who in turn gave them to Nimrod, and when the animals saw the latter clad in them, they crouched before him so that he had no difficulty in catching them. The people, however, thought that these feats were due to his extraordinary strength, so that they made him their king.
Nimrod is made king
According to another account, when Nimrod was eighteen years old, war broke out between the Hamites, his kinsmen, and the Japhethites. The latter were at first victorious, but Nimrod, at the head of a small army of Cushites, attacked and defeated them, after which he was made king over all the people on earth, appointing Terah his minister. It was then, elated by so much glory, that Nimrod changed his behavior toward God and became the most flagrant idolater. When informed of Abraham's birth he requested Terah to sell him the new-born child in order that he might kill it. Terah hid Abraham and in his stead brought to Nimrod the child of a slave, which Nimrod dashed to pieces.
Nimrod is generally considered to have been the one who suggested building the Tower of Babel and who directed its construction. According to the Talmud, God said: "I made Nimrod great; but he built a tower in order that he might rebel against Me". The tower is called by the Rabbis "the house of Nimrod," and is considered as a house of idolatry which the owners abandoned in time of peace; consequently Jews may make use of it. After the builders of the tower were dispersed Nimrod remained in Shinar, where he reestablished his kingdom. According to the "Sefer ha-Yashar", he at this time acquired the name "Amraphel" in allusion to the fall of his princes during the dispersion. According to the Targum of pseudo-Jonathan, however, Nimrod had left Babylonia before the building of the tower, and had gone to Assyria, where he built four other cities, namely, Nineveh, Rehobot, Calah, and Resen.
Nimrod in Islamic Literature
By the Muslims Nimrod is considered as the supreme example of the tyrant ("al-jabbar"). There is some confusion among Arabian historians as to Nimrod's genealogy. According to one authority he was the son of Mash the son of Aram, and consequently a Semite; he built the Tower of Babel and also a bridge over the Euphrates, and reigned five hundred years over the Nabatæans, his kinsmen. But the general opinion is that he was a Hamite, son of Canaan the son of Cush, or son of Cush the son of Canaan (Tabari gives both); that he was born at the time of Reu, and was the first to establish fire-worship. Another legend is to the effect that there were two Nimrods: the first was the son of Cush; the second was the well-known tyrant and contemporary of Abraham; he was the son of Canaan and therefore a great-grandson of the first Nimrod. According to Mas'udi, Nimrod was the first Babylonian king, and during a reign of sixty years he dug many canals in Iraq.
Nimrod and Abraham
The author of the "Ta'rikh Muntaḥab" (quoted by D'Herbelot in his "Bibliothèque Orientale") identifies Nimrod with Daḥḥak (the Persian Zoḥak), the first Persian king after the Flood. But Al-Kharizmi, identifies him with Kai Kaos, the second king of the second Persian dynasty. Nimrod reigned where Baghdad is now situated, and at first he reigned with justice; but Satan perverted him, and then he began to persecute all the worshipers of God. His chief vizier was Azar (Terah), the father of Abraham; and the midrashic legends of Abraham's birth in which Nimrod is mentioned, as well as those concerning Nimrod's persecution of Abraham—whom he cast into a furnace—are copied by the Mohammedans which some changes from Rabbinic Literature.
Nimrod is referred to in the Koran (xxi. 68-69). When Nimrod saw Abraham come unharmed from the furnace, he said to him: "Thou hast a powerful God; I wish to offer Him hospitality." Abraham told him that his God needed nobody's hospitality. Nevertheless Nimrod ordered thousands of horned and small cattle brought, and fowl and fish, and sacrificed them all to God; but God did not accept them. Humiliated, Nimrod shut himself in his palace and allowed no one to approach him. According to another tradition, Nimrod challenged Abraham, when the latter came out of the furnace, to fight with him. Nimrod gathered a considerable army and on the appointed day was surprised to find Abraham alone. Asked where his army was, Abraham pointed to a swarm of gnats, which routed Nimrod's troops (see, however, below). Nimrod assembled his ministers and informed them of his intention to ascend into the heavens and strike down Abraham's God. His ministers having told him that it would be difficult to accomplish such a journey, the heavens being very high, Nimrod conceived the idea of building a high tower, by means of which he might accomplish his purpose (comp. Sanh. 109a). After many years had been spent in the construction of the tower, Nimrod ascended to its top, but he was greatly surprised to find that the heavens were still as remote from him as when he was on the ground. He was still more mortified on the following day, when the tower collapsed with such a noise that the people fainted with terror, those that recovered losing their speech (an allusion to the confusion of tongues).
Undaunted by this failure, Nimrod planned another way to reach the heavens. He had a large chest made with an opening in the top and another in the bottom. At the four corners of the chest stakes were fixed, with a piece of flesh on each point. Then four large vultures, or, according to another source, four eagles, previously fed upon flesh, were attached to the stakes below the meat. Accompanied by one of his most faithful viziers, Nimrod entered the chest, and the four great birds soared up in the air carrying the chest with them. The vizier opened alternately the upper and lower doors of the chest in order that by looking in both directions he might know whether or not he was approaching heaven. When they were so high up that they could see nothing in either direction Nimrod took his bow and shot arrows into the sky. Gabriel thereupon sent the arrows back stained with blood, so that Nimrod was convinced that he had avenged himself upon Abraham's God. After wandering in the air for a certain length of time Nimrod descended, and the chest crashed upon the ground with such violencethat the mountains trembled and the angels thought an order from God had descended upon the earth. This event is alluded to in the Koran (xiv. 47): "The machinations and the contrivances of the impious cause the mountains to tremble." Nimrod himself was not hurt by the fall.
After these adventures Nimrod continued to reign wickedly. Four hundred years later an angel in the form of a man appeared to him and exhorted him to repent, but Nimrod declared that he himself was sole ruler and challenged God to fight with him. Nimrod asked for a delay of three days, during which he gathered a considerable army; but this was exterminated by swarms of gnats. One of these insects is said to have entered Nimrod's nose, reached the chambers of his brain, and gnawed at it. To allay the pain Nimrod ordered some one to strike with a hammer upon an anvil, in order that the noise might cause the gnat to cease gnawing. Nimrod died after forty years' suffering.