Assyrian captivity of Israel
The Northern Kingdom of Israel was conquered by the Neo-Assyrian monarchs, Tiglath-Pileser III (Pul) and Shalmaneser V. The later Assyrian rulers Sargon II and his son and successor, Sennacherib, were responsible for finishing the twenty-year demise of Israel's northern ten-tribe kingdom, although they did not overtake the Southern Kingdom. Jerusalem was besieged, but not taken. The tribes exiled by Assyria later became known as the Ten Lost Tribes.
And the Elohim of Israel stirred up a spirit of Pul king of Assyria, and the spirit of Tigathpileser king of Assyria, and he carried them away, even the Reubenites, and the Gadites, and the half tribe of Manasseh, and brought them unto Halah, and Habor, and Hara, and to the river Gozan, unto this day.(I Chronicles 5:26)
In the days of Pekah king of Israel came Tiglathpileser king of Assyria, and took Ijon, and Abelbethmaachah, and Janoah, and Kedesh, and Hazor, and Gilead, and Galilee, all the land of Naphtali, and carried them captive to Assyria.(II Kings)
In 722 BC, nearly twenty years after the initial deportations, the ruling city of the Northern Kingdom of Israel, Samaria, was finally taken by Sargon II after a three-year siege started by Shalmaneser V.
Against him came up Shalmaneser king of Assyria; and Hoshea became his servant, and gave him presents. And the king of Assyria found conspiracy in Hoshea: for he had sent messengers to So king of Egypt, and brought no present to the king of Assyria, as he had done year by year: therefore the king of Assyria shut him up, and bound him in prison. Then the king of Assyria came up throughout all the land, and went up to Samaria, and besieged it three years. In the ninth year of Hoshea the king of Assyria took Samaria, and carried Israel away into Assyria, and placed them in Halah and in Habor by the river of Gozan, and in the cities of the Medes.(II Kings 17:3-6)
And the king of Assyria did carry away Israel unto Assyria and put them in Halah and in Habor by the river of Gozan, and in the cities of the Medes: because they obeyed not the voice of the LORD their God, but transgressed his covenant, and all that Moses the servant of the LORD commanded and would not hear them, nor do them. (II Kings 18:11-12
The Book of Kings states several times that the entire people of the Kingdom of Israel had been taken into exile by the Assyrians. Some believe that the Books of Chronicles information about the fate of the Northern Kingdom adds up differently. What is often cited is 2nd Chronicles, Chapter 15, which mentions that there had been people from the hill-country cities of Ephraim and Manasseh who were captured by the Judean king, Asa of Judah. And Asa, sojourning among the Judean kingdom population, returned practicing the Hebrew belief. However, this is a mis-characterization of the events. Since those scriptures clearly declare that it was at a time when the Northern Kingdom was still intact, this happened in an era before the Assyrian Captivity.
And when Asa heard these words, even the prophecy of Oded the prophet, he took courage, and put away the detestable things out of all the land of Judah and Benjamin, and out of the cities which he had taken from the hill-country of Ephraim; and he renewed the altar of the LORD, that was before the porch of the LORD. And he gathered all Judah and Benjamin, and them that sojourned with them out of Ephraim and Manasseh, and out of Simeon; for they fell to him out of Israel in abundance, when they saw that the LORD his God was with him. So they gathered themselves together at Jerusalem in the third month, in the fifteenth year of the reign of Asa. (II Chronicles 15:8-10)
According to 2nd Chronicles, Chapter 30, there is evidence that at least some people of the Northern Kingdom of Israel were not exiled. These were invited by king Hezekiah to keep the Passover in a feast at Jerusalem with the Judean population. (The holiday was set one month forward from its original date.) Hezekiah sent his posts to spread the word among the remnant of the Northern kingdom; the posts were mocked during their visit to the country of Ephraim, Manasseh and Zebulun. However, some people of Asher and Manasseh and of Zebulun humbled themselves and came to Jerusalem. In a later part of the chapter, even people from the Tribe of Issachar and the strangers that "came out from the land of Israel" were said to take part in the passover event. Biblical scholars such as Umberto Cassuto and Elia Samuele Artom claimed that Hezekiah might have annexed these territories, in which inhabitants of the Kingdom of Israel remained, into his own kingdom.
And Hezekiah sent to all Israel and Judah, and wrote letters also to Ephraim and Manasseh, that they should come to the house of the LORD at Jerusalem, to keep the passover unto the LORD, the God of Israel. (II Chronicles 30:1)
So they established a decree to make proclamation throughout all Israel, from Beer-sheba even to Dan, that they should come to keep the passover unto the LORD, the God of Israel, at Jerusalem; for they had not kept it in great numbers accordingly, as it is written. So the posts went with the letters from the king and his princes throughout all Israel and Judah, according to the commandment of the king, saying: 'Ye children of Israel, turn back unto the LORD, the God of Abraham, Isaac, and Israel, that He may return to the remnant that are escaped out of the hand of the kings of Assyria. And be ye not like your fathers and like your brethren who acted treacherously against the LORD, the God of their fathers, so that He delivered them to desolation, as ye see. Now be ye not stiffnecked as your fathers were, but yield yourselves unto the LORD and enter into His sanctuary which He hath sanctified for ever; and serve the LORD your God that His fierce anger may turn away from you. For if ye turn back unto the LORD, your brethren and your children shall find compassion before them that led them captive, and shall come back into this land; for the LORD your God is gracious and merciful, and will not turn away His face from you if ye return unto Him.' (II Chronicles 30:5-9)
So the posts passed from city to city through the country of Ephraim and Manasseh, even unto Zebulun; but they laughed them to scorn, and mocked them. Nevertheless certain men of Asher and Manasseh and of Zebulun humbled themselves, and came to Jerusalem.(II Chronicles 30:11-12)</
For a multitude of the people, even many of Ephraim and Manasseh, Issachar and Zebulun, had not cleansed themselves, yet did they eat the passover otherwise than it is written. For Hezekiah had prayed for them, saying: 'The good LORD pardon...' (II Chronicles 30:18)
So there was great joy in Jerusalem; for since the time of Solomon the son of David king of Israel there was not the like in Jerusalem. (II Chronicles 30:25-26)
And all the congregation of Judah, with the priests and the Levites, and all the congregation that came out of Israel, and the strangers that came out of the land of Israel, and that dwelt in Judah, rejoiced.
In 2nd Chronicles, Chapter 31, it is said that the remnant of the Kingdom of Israel returned to their homes, but not before destroying Ba'al and Ashera places of Idol worship left in "all Judah and Benjamin, in Ephraim also and Manasseh".
Now when all this was finished, all Israel that were present went out to the cities of Judah, and broke in pieces the pillars, and hewed down the Asherim, and broke down the high places and the altars out of all Judah and Benjamin, in Ephraim also and Manasseh, until they had destroyed them all. Then all the children of Israel returned, every man to his possession, into their own cities. (II Chronicles 31:1)
Sargon records his first campaign on the walls of the royal palace at Dur-Sharrukin (Khorsabad):
In my first year of reign *** the people of Samaria *** to the number of 27,290 ... I carried away.
Fifty chariots for my royal equipment I selected. The city I rebuilt. I made it greater than it was before.People of the lands I had conquered I settled therein. My official (Tartan) I placed over them as governor. (L.ii.4.) 
The description of the final defeat of the Northern Kingdom of Israel above appears to be a minor event in Sargon's legacy. Some historians attribute the ease of Israel's defeat to the previous two decades of invasions, defeats, and deportations.
Some estimates assume a captivity numbering in the hundreds of thousands, minus those who died in defense of the kingdom and minus those who fled voluntarily before and during the invasions.
However, it has also been suggested that the numbers deported by the Assyrians were rather limited and the bulk of the population remained in situ. There is also evidence that significant numbers fled south to the kingdom of Judah.
Unlike the Kingdom of Judah, which was able to return from its Babylonian Captivity, the ten tribes of the Northern Kingdom never had a foreign edict granting permission to return and rebuild their homeland. Many centuries later, rabbis of the restored Kingdom of Judah were still debating the return of the lost ten tribes. However, Assyria had been conquered by Babylon, and Babylon had been conquered by the Medo-Persians.
However, according to the Books of Chronicles chapter 9 line 3, the Israelites, who took part in The Return to Zion, are stated to be from the Tribe of Judah alongside the Tribe of Simeon that was absorbed into it, the Tribe of Benjamin, the Tribe of Levi (Levites and Priests) alongside the tribes of Ephraim and Manasseh, which according to the Book of Kings 2 Chapter 7 were supposely exiled by the Assyrians (The Biblical scholars Umberto Cassuto and Elia Samuele Artom claimed these two tribes' names to be a reference to the remant of all Ten Tribes that was not exiled and absorbed into the Judean population).
And in Jerusalem dwelt of the children of Judah, and of the children of Benjamin, and of the children of Ephraim and Manasseh. This particular verse is often misconstrued, since the obvious declaration being made in I Chronicles are that of a genealogical reference. The clear indication is seen when directing the readers attention to I Chronicles when mentioning the Nethinims of which were a people conquered by Joshua (Joshua 9:27. This thereby dictates that it's referring to a completely different time and era, as further seen with the description in verse 2 where it indicates that the Israelites were gaining their land designated possessions attributed to their God YHWH and his General in charge Joshua.(I Chronicles)
The scriptures of the titled "Old Testament" are not accurately complete without the records of those Hebrew writers that penned them. This points to the complete records that declare the clarity of the Grecian conquests of the Judeans during and after the reign of Alexander, as indicated by the book of Maccabbees. The historical accuracy by the prophet Ezra is complete only when the details of the Apocrypha's 1st and 2nd Esdras are referenced, since there is where the complete history of the dispersion of the Northern Kingdom tribes is seen, in 2 Esdras 13:40-48 
New names Theory
Two centuries after their exile, there have been theories that they were temporarily conquered again under different names at the hands of a different empire, Persia. This is the mid-19th century interpretation of the Behistun Inscription, King Darius's record of his conquered, by the famous transcriber and translator of the inscription George Rawlinson:
“We have reasonable grounds for regarding the Gimirri, or Cimmerians, who first appeared on the confines of Assyria and Media in the seventh century B.C., and the Sacae of the Behistun Rock, nearly two centuries later, as identical with the Beth-Khumree of Samaria, or the Ten Tribes of the House of Israel.”
- Babylonian Captivity
- Kingdom of Israel
- History of ancient Israel and Judah
- Lost Tribes of Israel
- The Books of Kings and Chronicles modern view by Umberto Cassuto and Elia Samuele Artom (1981)
- Luckenbill, Daniel David. Ancient Records of Assyria and Babylon ISBN 1-85417-049-X
- Mishnah, Sanhedrin 110b
- George Rawlinson, note in his translation of History of Herodotus, Book VII, p. 378