Amalek
Amalek is the grandson of Esau, the son of Eliphaz by his concubine Timna (Gen 36:12; 1Ch 1:36). His name then attaches to the people descended from him, who first appear as a country struck during the campaign of the eastern kings (Gen 14:7) and reappear as Israel's archetypal enemy from the Exodus onward.
Origin in the Esau Line
The genealogy places Amalek squarely inside the Edomite branch of Abraham's family. "And Timna was concubine to Eliphaz Esau's son; and she bore to Eliphaz Amalek: these are the sons of Adah, Esau's wife" (Gen 36:12). The same line is repeated in the Chronicler's roster: "The sons of Eliphaz: Teman, and Omar, Zephi, and Gatam, Kenaz, and Timna, and Amalek" (1Ch 1:36).
The country of the Amalekites is also named earlier, before Amalek the person is born in narrative time: in the war of the kings, the invaders "returned, and came to En-mishpat (the same is Kadesh), and struck all the country of the Amalekites, and also the Amorites, who dwelt in Hazazon-tamar" (Gen 14:7). The territory carries the name forward.
The Battle at Rephidim
Amalek as a hostile people first confronts Israel just after the Exodus: "Then came Amalek, and fought with Israel in Rephidim" (Ex 17:8). The encounter sets the long-running posture between the two peoples.
The Standing Charge in Deuteronomy
Moses' farewell discourse fixes the memory of Amalek's attack as a permanent obligation:
"Remember what Amalek did to you by the way as you⁺ came forth out of Egypt; how he met you by the way, and struck the hindmost of you, all who were feeble behind you, when you were faint and weary; and he didn't fear God. Therefore it will be, when Yahweh your God has given you rest from all your enemies round about, in the land which Yahweh your God gives you for an inheritance to possess it, that you will blot out the remembrance of Amalek from under heaven; you will not forget" (Dt 25:17-19).
Two motives are stacked together: Amalek's predation on the weakest in the column, and his lack of fear of God. The remedy is total — blot out the remembrance — and the trigger is delayed until Israel has rest in the land.
Saul's Failure
The charge passes to Saul as a specific war: "Now go and strike Amalek, and completely destroy all that they have, and don't spare them; but slay both man and woman, infant and suckling, ox and sheep, camel and donkey" (1Sa 15:3). Saul's incomplete obedience is later named as the reason his kingdom is taken: "Because you didn't obey the voice [Speech] of Yahweh, and did not execute his fierce wrath on Amalek, therefore has Yahweh done this thing to you this day" (1Sa 28:18).
David and the Amalekites
The charge falls in part to David. The opening of 2 Samuel marks a return from such a campaign: "And it came to pass after the death of Saul, when David returned from the slaughter of the Amalekites, and David had remained two days in Ziklag" (2Sa 1:1).
The Last Remnant
The Chronicler records the final reduction in the days of Hezekiah, when the Simeonites moved into the hill country of Seir: "And they struck the remnant of the Amalekites who escaped, and have dwelt there to this day" (1Ch 4:43). The blotting-out commanded in Deuteronomy reaches its end-point in this notice.