The Moabites originated from Lot, a nephew of Abraham (see also Abraham Wasn't A Jew).
"19:36 Thus were both the daughters of Lot with child by their father. 19:37 And the firstborn bare a son, and called his name Moab: the same is the father of the Moabites unto this day. 19:38 And the younger, she also bare a son, and called his name Benammi: the same is the father of the children of Ammon unto this day." (Genesis 19:36-38 KJV)
Later, a well-known ancestor of King David (see Israelite Monarchy - The Origin, The Civil War and The United Kingdom) was Ruth, a Moabite who had moved with Naomi back to the land of Judah.
"1:3 And Elimelech Naomi's husband died; and she was left, and her two sons. 1:4 And they took them wives of the women of Moab; the name of the one was Orpah, and the name of the other Ruth: and they dwelled there about ten years." (Ruth 1:3-4 KJV)
"4:13 So Boaz took Ruth, and she was his wife: and when he went in unto her, the LORD [see 'Before Abraham Was, I AM'] gave her conception, and she bare a son ... and they called his name Obed: he is the father of Jesse, the father of David" (Ruth 4:13,17 KJV)
"And so the Moabites became David's servants"
The Moabites did not always fare well with Ruth's great-grandson David (David was the son of Jesse, who was the son of Obed, who was the son of Ruth). The Moabites (whose territory was centered in what is today part of the kingdom of Jordan) were subject to imperial Israel, along with a number of other nations in the region. David became the emperor (i.e. the leader of an empire, from which the world imperialism is based) of all of those nations.
"8:1 And after this it came to pass, that David smote the Philistines, and subdued them: and David took Methegammah out of the hand of the Philistines.
8:2 And he smote Moab, and measured them with a line, casting them down to the ground; even with two lines measured he to put to death, and with one full line to keep alive. And so the Moabites became David's servants, and brought gifts.
8:3 David smote also Hadadezer, the son of Rehob, king of Zobah, as he went to recover his border at the river Euphrates. 8:4 And David took from him a thousand chariots, and seven hundred horsemen, and twenty thousand footmen: and David hocked all the chariot horses, but reserved of them for an hundred chariots.
8:5 And when the Syrians of Damascus came to succour Hadadezer king of Zobah, David slew of the Syrians two and twenty thousand men. 8:6 Then David put garrisons in Syria of Damascus: and the Syrians became servants to David, and brought gifts. And the LORD preserved David whithersoever he went." (2 Samuel 8:1-6 KJV)
The empire of Israel continued and expanded even further under David's son Solomon.
"4:20 Judah and Israel were many, as the sand which is by the sea in multitude, eating and drinking, and making merry.
4:21 And Solomon reigned over all kingdoms from the river unto the land of the Philistines, and unto the border of Egypt: they brought presents, and served Solomon all the days of his life." (1 Kings 4:20-21 KJV)
"10:14 Now the weight of gold that came to Solomon in one year was six hundred threescore and six talents of gold, 10:15 Beside that he had of the merchantmen, and of the traffic of the spice merchants, and of all the kings of Arabia, and of the governors of the country." (1 Kings 10:14-15 KJV)
"10:1 And when the queen of Sheba heard of the fame of Solomon concerning the name of the LORD, she came to prove him with hard questions. 10:2 And she came to Jerusalem with a very great train, with camels that bare spices, and very much gold, and precious stones: and when she was come to Solomon, she communed with him of all that was in her heart. 10:3 And Solomon told her all her questions: there was not any thing hid from the king, which he told her not.
10:4 And when the queen of Sheba had seen all Solomon's wisdom, and the house that he had built, 10:5 And the meat of his table, and the sitting of his servants, and the attendance of his ministers, and their apparel, and his cupbearers, and his ascent by which he went up unto the house of the LORD; there was no more spirit in her. 10:6 And she said to the king, It was a true report that I heard in mine own land of thy acts and of thy wisdom." (1 Kings 10:1-6 KJV)
Fact Finder: After the Messiah's return, the entire world will be ruled by Jesus Christ (see also The Coming World Dictator). What will King David be doing then?
See David, Future King Of Israel