Iphigenia in Taurus takes place in a temple to the goddess Artemis along the shore of Taurus. It opens with a prologue spoken by one of the main characters, Iphigenia. In Euripidean prologues, the events preceding the story are recounted and the upcoming action foretold. Iphigenia explains why she was yet alive after ostensibly being sacrificed by her father, Agamemnon, who offered his child in order to dispel storms preventing his fleet from departing for an important battle.

Artemis, the virgin goddess of childbirth, had once extracted from Agamemnon the promise to sacrifice the loveliest creature born in a twelve month period. His wife Clytemnestra had borne Iphigenia, and Artemis demanded her blood. Agamemnon contrived a false pretext for stealing his daughter, asking Clytemnestra to prepare the child to wed Achilles. But once on the altar of sacrifice, Artemis snatched the young maiden away, placing a deer in her place to fool the humans. Artemis magically transported Iphigenia to Taurus, a "barbarian'' land and made her a priestess in her temple. Ironically, Iphigenia often prepares her fellow Hellenes for sacrifice upon the shrine.

Iphigenia further relates a strange dream she had the previous night, in which an earthquake crumbled her father's house and left only one column standing. This column wore brown hair and Iphigenia weeped over it and prepared it for the deadly ritual of Artemis's temple. Iphigenia interprets her dream to mean that her brother, Orestes, has died and that she cannot properly bury him. She retreats into the temple to pour libations for him.

As she departs, Orestes and his friend Pylades enter from the ocean shore. He and Pylades have been sent by the oracle of Phoebus in retribution for avenging his father's death by killing his mother, Clytemnestra (who killed Agamemnon because he sacrificed Iphigenia). Phoebus, the sister of Artemis, has ordered Orestes to steal her statue from Artemis's temple and give it to Athens. Only by this act of courage will Orestes be freed from the furies who have pursued him since he killed his mother. The two friends discuss how they can accomplish their mission and decide to hide in the caves of the sea cliffs until nightfall.

The chorus enters and sings of Artemis's temple and rituals. These are the girls who assist Iphigenia in her ritual preparations, and she shares with them her interpretation of her dream. They echo her mourning chant and then draw her attention to some herdsmen approaching the temple. The herdsmen explain to Iphigenia that while driving their cattle to the seashore to wash them, they saw two young Hellene men in one of the sea caves. They decided to capture the two to sacrifice to Artemis, according to their local custom. Then one of the strangers began to babble like a madman about "fiends from Hades'' attacking him (this is the work of the furies that torment Orestes). Orestes slays some of the cattle, thinking they are the furies, and the herdsmen respond by stoning the two and taking them as prisoners to the king. The king ordered the prisoners sent to Iphigenia for purification and then sacrifice. Iphigenia commands the men brought before her; the "loss'' of her brother makes her eager to sacrifice these two strangers.

Iphigenia once again recalls the horror of her aborted sacrifice, this time mentioning poignant details that create empathy with the audience, as she addresses the chorus. She ends by saying she believes the gods could not have caused her pain— that men blame the gods for their own evil actions. The chorus supports her prayer to return to her home in Athens. In appraising the two approaching Hellenes, the chorus indirectly reminds the audience that human sacrifice is not allowed by Hellenic law.
Iphigenia has the prisoners unbound while she interrogates them about their identity and the events back in Athens. Out of pride, Orestes refuses to tell his name. He even recounts the story of murdering Clytemnestra as though another committed the act and speaks of himself in third person. There are moments when the audience understands the dramatic irony of comments such as Iphigenia's wish that her own brother might be as noble as the man standing before her and Orestes's wish that his sister might be the one to purify him before his sacrifice.

The pair earns Iphigenia's respect, so she devises a plan to let one of them go, as long as he carries a message back to her brother. When she leaves to get the letter, Orestes and Pylades remark on her knowledge of their city. It seems as though they might recognize who she is, but instead Pylades expresses concern that he will be accused of killing Orestes. Iphigenia returns and she and Pylades trade oaths that they will accomplish what they promise. Pylades will go free and deliver the letter.

To assure that Pylades cannot fail by losing the letter, she has him memorize it. It is during the recitation of the letter that the two men recognize Orestes's sister. Orestes turns in joy to Iphigenia, but the chorus accuses him of desecrating her holy robes. Iphigenia demands proof that he truly is his brother and is not merely trying to trick her so that he may go free. When he proves himself, Iphgenia bemoans the crimes she nearly committed.

After Iphigenia explains how it is that she is still alive, the three strategize an escape plan. They cannot kill the king because that would violate the "law of guest and host.'' Iphigenia devises a plan to pretend that they have desecrated the statue Orestes must steal. She will tell Thoas that she must cleanse it and the two prisoners in the sea. That will allow them to make a run for Orestes's ship. Iphigenia prays to Artemis for help, and the chorus sings encouragement.

King Thoas enters with his guards asking the whereabouts of Iphigenia. She enters with the statue and silences him with the news that "impurity'' has violated it. He agrees to honor her desire to purify it, after hearing her say the prisoners are guilty of horrific deeds at home. Her demand for solitude during the purification does not make him suspicious because she asks him to purify the temple with fire while she is busy at the sea. Keeping onlookers away from the unholy statue, she makes her way to the sea with her two "prisoners'' The chorus sings the story of Artemis and Phoebus, ending with a story about the unreliability of dream interpretation.

A messenger rushes up to tell King Thoas that the two prisoners have fled in their ship, along with Iphigenia. Despite the trio's successful getaway, the ship is in danger of grounding near shore. Thoas orders horsemen to capture them, but he is stopped by Athena, goddess of reason, who informs the king that Apollo wants Orestes to convey the holy image to Athens. Athena orders the end of human sacrifice and decrees that all accused will be given the benefit of a fair trial in which a majority vote will decide their fate—treatment that Orestes received when he was judged for Clytemnestra's murder. Thoas agrees, and Athena applauds his decision, saying that even the gods must end to Necessity.