Epithets in the Iliad and the Odyssey, unsurprisingly also known as Homeric epithets, one of Homer's methods to identify the multitude of gods and mortals in the poem, may have originated as a feature of the original oral poem that we know as the Iliad. Epithets serve to remind the listeners (and readers) of key characteristics of mortals and gods—"rosy-fingered Dawn," for example—and they may have allowed the poet to "even out" a line of verse when an individual's name alone interfered with the meter and, because they were formulaic, they helped the poet remain consistent throughout many recitations. In the Iliad, epithets tend to express an individual's lineage—"Achilles, son of Peleus"—or an important personal attribute—"crafty-minded Odysseus."
Another, and perhaps more interesting, technique is Homer's use of dramatic scenes in which otherwise static individuals become dynamic. Ajax the Greater, also often referred to as Ajax, son of Telamon, is a good example. Throughout most of the Iliad, Ajax is seen only as one of the Greeks' strongest warriors but not as particularly bright, while in Book IX, when Odysseus, Phoenix, and Ajax are trying to convince Achilles to get back into the fight, Ajax is the most successful of all when he reminds Achilles that his refusal to support the Greeks is illogical. Agamemnon has taken one slave girl from Achilles, and now, Ajax and the other emissaries are offering seven to replace one, and still Achilles refuses:
But obdurate and malign / is the spirit the gods have put in your breast, and all because / of just one girl! Yet, now, we're ready to give you seven, / the best there are, and much else besides! (IX:636-639)
Ajax's appeal to Bronze Age warrior arithmetic is obviously effective because Achilles acknowledges that "I, too, have been thinking along those lines." Despite this, however, Achilles' hatred of Agamemnon's taking of Briseis is overwhelming and he refuses the offer. This scene is one of only a few in which Ajax becomes something more than just a great instrument of destruction but is typical of the care with which the poet adds to an individual's identity.
In Book XXIV, another scene turns Achilles from a warrior into a sympathetic man. After Hector's death at Achilles' hands, Priam, whose epithet is routinely "god-like," sneaks into Achilles's camp to beg Achilles to return Hector's body for proper burial. Priam's argument is that he is an old man whose only goal is to care for his dead son, and he tells Achilles that his father, Peleus, must have the same fears as Priam—not knowing whether his son is dead or alive or whether he (Achilles) will receive a proper burial. This is a remarkable moment because Achilles breaks down, cries, and comforts Priam, one of only two times that Achilles is seen to grieve for another. Achilles then allows Priam to stay in his tent until morning and allows him to take Hector's body to Troy for burial, which is a very important rite for a Bronze Age warrior.
Homer's scenes in which key individuals interact to discuss profound issues allows the accretion of individual attributes that change key characters from static or stock characters to fully rounded individuals.