The nation of Israel was to be His royal priesthood nation upon earth (Exodus 19:3-6), a light to the nations of the world. For this reason they were given His holy precepts to live by so that all the world could see the benefits of living according to the Holy One's standards for mankind. As His spiritual children, He taught them and trained them and when necessary He disciplined them.
The Almighty God, Yahweh, entered into covenant relationship with Abraham, Yitzak (Isaac) and Ya'acov (Jacob) to establish His purposes in the earth. Through Moshe (Moses), He called them to account that (in His faithfulness to them), He would execute judgment upon them if they rebelled against Him (Leviticus 26); and so He did.
The nation was formed by the twelve sons of Ya'acov (Jacob). Israel became a nation at the Exodus when they came out of their sojourn in Egypt. In the wilderness they were given a divine placement around the Tabernacle which served as their order of rank for divine service. This was the blueprint for the endtime function of his priesthood nation in the earth and is seen in its final image in the New Jerusalem (Revelation 21) Each tribe stands there in a place of authority at the gates, as king/priests, forming the government of the new earth.
In the process of time, the nation formed two Houses through a division of the tribes into two groups. The northern tribes separated from the kingship under the tribe of Judah and became autonomous (1 Kings 12). That left two tribes, plus the tribe of Benjamin to the House of Yehudah (Judah) and 10 tribes to the northern kingdom which became known as the House of Ephraim/House of Israel.
After the division, some scriptures are addressed to both Houses and many others are addressed to one or the other, as Yahweh treated them separately. The House of Ephraim came under judgment and was divorced for her spiritual adultery and apostasy and was carried away captive by Assyria in the years between 722 - 740BC. The House of Yehudah was judged also, but not divorced and went into captivity for 70 years by Babylon. A remnant returned and became the people-group identified as the "Jews" at Yeshua's time.
The greater part of the House of Yehudah (now known as Jews) stayed in the dispersion in the kingdom of Babylon and later moved to other areas.
The ten northern tribes were never returned to the land and remained dispersed among the nations where they were carried captive, fleeing from place to place, and in time (for the most part) lost their identity as the children of Israel.
But there is to come a restoration! The eternal plan of Almighty God will have its fulfilment in spite of the shortcomings and iniquities of His people. A remnant will return! A remnant will enter in to become His kingdom of priests upon earth.