[1] The play depicts the fate of the warrior Ajax the Great, the second greatest hero at Troy (after Achilles), after the events of the Iliad but before the end of the Trojan War.

The play opens with a dialogue between Athena and Odysseus: After the great warrior Achilles had been killed in battle, there was a question as to who should receive his armor.

As the man who now could be considered the greatest Greek warrior, Ajax felt he should be given Achilles' armor, but the two kings, Agamemnon and Menelaus, awarded it instead to Odysseus.

[6] Ajax, as he appears in this play, in the Iliad, and other myths, is a heroic figure, a "rugged giant", with strength, courage and the ability to think quickly well beyond the normal standards of mankind.

[7] Hugh Lloyd-Jones points out that many authorities consider Ajax an early play, but he suggests that if the text excludes material that he has bracketed, then it would seem to be a "mature masterpiece, probably not much earlier than Oedipus Tyrannus".

Bagg and Scully consider that the play, with its two parts, may be seen as an important epoch-spanning work that raises complex questions, including: How does 5th-century Greece advance from the old world into the new?

As Bagg and Scully contend, Ajax, with his brute force has been a great warrior-hero of the old world, but the Trojan war itself has changed and become a quagmire; what's needed now is a warrior who is intelligent – someone like Odysseus.

[11] John Moore interprets the play as primarily a character study of Ajax, who, when he first appears covered in the blood of the animals that he in his madness has killed, presents an image of total degradation; the true action of the play, according to Moore, is how this image is transformed from degradation, as Ajax recovers his heroic power and humanity.

[12] Translators Frederic Raphael and Kenneth McLeish called the work a "masterpiece", arguing that "Sophocles turned the almost comic myth of a bad loser into a tragedy of disappointment, folly, and divine partiality.

"[14] The speech begins: Long rolling waves of time bring all things to light and plunge them down again in utter darkness.

[16] The American director Peter Sellars staged an adaption of the play, also called Ajax, written by Robert Auletta at the Kennedy Center in Washington, D.C. and at the La Jolla Playhouse in San Diego in 1986.

[17][18] Ajax was produced at the American Repertory Theater in Cambridge in 2011, in modern dress, with a setting that appeared to be a war zone somewhere in the Middle East.

[19] In May 2016, Jeff S. Dailey directed the play for a limited Off Broadway run at the John Cullum Theatre in midtown Manhattan.

[20][non-primary source needed] It set the play Sophocles' original location of Troy and featured Matthew Hansen in the title role.