The area of Medeba was taken by the Israelites after Sihon king of the Amorites opposed their request to peacefully pass through his territory:
"But Sihon would not allow Israel to pass through his territory. He gathered all his men together, and went out against Israel to the wilderness, and came to Jahaz, and fought against Israel. And Israel slew him with the edge of the sword, and took possession of his land from the Arnon to the Jabbok, as far as to the Ammonites; for Jazer was the boundary of the Ammonites. And Israel took all these cities, and Israel settled in all the cities of the Amorites, in Heshbon, and in all its villages. For Heshbon was the city of Sihon the king of the Amorites, who had fought against the former king of Moab and taken all his land out of his hand, as far as the Arnon."
"Therefore the ballad singers say, "Come to Heshbon, let it be built, let the city of Sihon be established. For fire went forth from Heshbon, flame from the city of Sihon. It devoured Ar of Moab, The Lords of the heights of the Arnon. Woe to you, O Moab! You are undone, O people of Chemosh! He has made his sons fugitives, and his daughters captives, to an Amorite king, Sihon. So their posterity perished from Heshbon, as far as Dibon, and we laid waste until fire spread to Medeba." Thus Israel dwelt in the land of the Amorites" (Numbers 21:21-31 RSV)
Medeba was included in the land assigned to the tribe of Reuben:
"And Moses gave an inheritance to the tribe of the Reubenites according to their families. So their territory was from Aroer, which is on the edge of the valley of the Arnon, and the city that is in the middle of the valley, and all the tableland by Medeba; with Heshbon, and all its cities that are in the tableland" (Joshua 13:15-17 RSV)
In the time of King David, it was at Medeba that Joab defeated the Ammonites and their allies:
"And David's servants came to Hanun in the land of the Ammonites, to console him. But the princes of the Ammonites said to Hanun, "Do you think, because David has sent comforters to you, that he is honoring your father? Have not his servants come to you to search and to overthrow and to spy out the land?" So Hanun took David's servants, and shaved them, and cut off their garments in the middle, at their hips, and sent them away; and they departed."
"When David was told concerning the men, he sent to meet them, for the men were greatly ashamed. And the king said, "Remain at Jericho until your beards have grown, and then return."
"When the Ammonites saw that they had made themselves odious to David, Hanun and the Ammonites sent a thousand talents of silver to hire chariots and horsemen from Mesopotamia, from Arammaacah, and from Zobah. They hired thirty-two thousand chariots and the king of Maacah with his army, who came and encamped before Medeba. And the Ammonites were mustered from their cities and came to battle."
"When David heard of it, he sent Joab and all the army of the mighty men. And the Ammonites came out and drew up in battle array at the entrance of the city, and the kings who had come were by themselves in the open country."
"When Joab saw that the battle was set against him both in front and in the rear, he chose some of the picked men of Israel, and arrayed them against the Syrians; the rest of his men he put in the charge of Abishai his brother, and they were arrayed against the Ammonites. And he said, "If the Syrians are too strong for me, then you shall help me; but if the Ammonites are too strong for you, then I will help you. Be of good courage, and let us play the man for our people, and for the cities of our God; and may The Lord do what seems good to him."
"So Joab and the people who were with him drew near before the Syrians for battle; and they fled before him." (1 Chronicles 19:1-14 RSV)
Fact Finder: Was Medeba included in Isaiah's lament for Moab?