The core biographical record of Abraham's old age runs through the pesukim themselves: he was already called old, advanced in years, together with Sarah before Isaac's birth (Bereishit 18:11, Bereishit 18:12-14), he received the covenant and the promise of fatherhood at ninety-nine (Bereishit 17:1-8), he sent his servant on the mission to find a wife for Isaac explicitly because he was old, advanced in days (Bereishit 24:2-4), he took another wife and fathered more children and distributed gifts to his sons while still alive in his later years (Bereishit 25:1-6), Isaac himself is called a son of his old age (Bereishit 21:2), and his life closes with him dying at a good old age, old and contented (Bereishit 25:7-8). Also bound up in this later-life record are his departure at the start of his journey (Bereishit 12:1) and his mourning and burial dealings for Sarah (Bereishit 23:1-20).
Chazal develop a recurring theme that old age as a visible, recognizable phenomenon did not exist before Abraham and that he himself requested it so that father and son could be told apart, a request God granted starting from him, as reflected in the phrase "and Abraham was old, advanced in days" (Bereshit Rabbah 65:9, Midrash Tanchuma, Noach 14:2, Various midrashim, Bereishit Rabbah 48:16, Bava Kamma 97b). This same point is read out of the sugya and developed by later commentators: that old age was unrecognized until Abraham prayed for it (Chiddushei Aggadot, Bava Metzia 86, Chiddushei Aggadot, Bava Kamma 41), and the Maayan Omer brings the Gemara's teaching that old age did not previously exist and that Abraham prayed for it, reading this out of the words "and Abraham was old, advanced in days" (Rav Ovadia Yosef (Maayan Omer 12:1:45)).
Rav Ovadia Yosef (Maayan Omer 12:1:44) likewise addresses this same teaching of the Gemara that old age did not exist prior to Abraham and that he prayed for it, grounding the point in the phrase "and Abraham was old, advanced in days."
Bereishit Rabbah 59:6 elaborates that Abraham's being called "zaken" means he acquired two worlds, and that unlike others whose appearance of age does not match their actual length of days, in Abraham the two matched perfectly, so that his advanced appearance corresponded to his advanced years (Bereishit Rabbah 59:6), and Berakhot notes that he grew from being father to Aram alone into being father to the whole world (Berakhot 13a).
The classical meforshim on "and Abraham was old, advanced in days" explain his concern in his later years for arranging Isaac's marriage before his own death: the Ramban says Abraham, seeing himself very old, feared he might die before the servant's mission to find Isaac a wife was complete, and so bound him by oath (Ramban on Bereishit 24:1); the Sforno similarly explains that his old age made him anxious he would die without seeing his son married (Sforno on Bereishit 24:1); and the Or HaChaim adds that, seeing both his age and his great wealth, he feared his powerful servant might scheme to marry his own daughter to Isaac, prompting the oath (Or HaChaim on Bereishit 24:1). Rashi, commenting on the span of Abraham's life, explains that at one hundred he was like a seventy-year-old, and at seventy like a five-year-old free of sin, a mark of his good old age (Rashi on Bereishit 25:7), while the Ramban on his death explains "old and content" as meaning he had seen all his heart's desires fulfilled and his soul was sated with days, wanting nothing more that further days might bring (Ramban on Bereishit 25:8).
Rav Samson Raphael Hirsch reads "zaken" as denoting one of mature, settled understanding, in contrast to the youth who easily sheds impressions received from outside (Rav Samson Raphael Hirsch).
Other sources trace the practical and chronological contours of Abraham's later years: the Seder Olam Rabbah maps out his ages at the covenant between the parts, his descent to Charan, Egypt, and the war of the kings (Seder Olam Rabbah 1:2); the Pesikta Rabbati likewise situates him at seventy at the covenant between the parts and at one hundred when Isaac was born (Pesikta Rabbati 42); and Beit Yaakov HaKolel notes that he lived forty-eight years after Sarah's death, continuing to receive support despite losing hers (Beit Yaakov HaKolel p. 18), while elsewhere reading "Abraham was old" as describing the honor and splendor of gray hair, old age as a crown bound up with wisdom in deeds (Beit Yaakov HaKolel p. 20).
Several sources treat specific events of Abraham's old age: the feast he made when Isaac was weaned, at which the nations mocked the old man and old woman claiming a foundling as their son (Bava Metzia 87a, Sulam on Zohar, Introduction 177); the Malbim's comment that the miracle recognized at that feast was not merely that Abraham fathered a child in his old age, which had been promised, but that Sarah had milk to nurse, an unpromised wonder given only for the world's rejoicing (Malbim on Bereishit 21:7:1); and the Etz Yosef's observation that Abraham, despite his old age, circumcised himself though the mark would scarcely have been noticed (Etz Yosef on Devarim Rabbah 6:1:2).
Halachic and chassidic literature also draws on the phrase describing Abraham's old age: the Sdei Chemed surveys various definitions of "zaken" in terms of age thresholds (Sdei Chemed, Maarechet Zayin 17); the Kitzur Shulchan Arukh brings the custom of reciting the pasuk "and Abraham was old, advanced in days" after Hallel as a segulah (Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim 422:20); and a chassidic discourse interprets his being "old, advanced in days" as a blessing bound up with his own spiritual labor, in contrast to the blessing of "all," which the pasuk attributes to God directly, concluding that the sequence of blessings follows from his having stood firm through ten trials (Maamarim Melukatim, ש"פ חיי שרה, מבה"ח כסלו ה'תשל"ז). Hegyonot El Ami, Volume II, Chayei Sara 21:1 likewise takes up Abraham in his old age as its subject.