The Greek army has besieged the ancient walled city of Troy for 10 years. The war began when Helen of Sparta abandoned her husband Menelaus for the Trojan Prince Paris, son of King Priam. Menelaus’ brother, Agamemnon, commands the Greek army that surrounds Troy and has besieged it for a decade, seeking to increase his power through a war based on this adulterous liaison.
On the plains just outside Troy the Greek warrior Achilles slays the Trojan Hector, another son of King Priam, when the materialization of the TARDIS disturbs Hector’s concentration. When the Doctor emerges from within the TARDIS, Achilles believes him to be the god Zeus disguised as an old beggar, and insists he accompany him to the Greek encampment. En route they encounter the sailor warrior Odysseus (from Odyssey), who travels with them to the Greek camp. When they arrive there, Agamemnon insists the Doctor, being Zeus, help him against the Trojans and will not let him depart until his aid is forthcoming. Odysseus is more sceptical, disbelieving Achilles, and branding the Doctor a Trojan spy.
The Doctor’s companions Vicki and Steven have watched him being led away. Vicki still has an injured ankle from a previous adventure in Galaxy Four, so Steven ventures out alone to try and help the Doctor. He is spotted heading for the Trojan camp by Cyclops, a mute servant of Odysseus, who reports this to his master. Odysseus soon catches Steven and takes him to the Greek camp as well, where the two prisoners must pretend they do not know each other in order to maintain the Doctor's guise as Zeus. The Doctor eventually persuades the Greeks to spare Steven until the next morning when he, as Zeus himself, will strike down "the spy" with a heavenly thunderbolt. Moments later Cyclops returns to the Greek camp, and through sign language communicates that Zeus’ temple (the TARDIS) has disappeared from the plains of Troy.
The next morning, the Doctor and Steven travel with the Greeks to the plains and discover the TARDIS has indeed disappeared. The Doctor confesses that he and Steven are indeed friends and not gods in disguise. Odysseus decides to let them live, but demands that their powers be used to destroy the Trojans within two days, or they will be killed. Steven privately suggests to the Doctor that they use the Trojan Horse of myth, but the Doctor is reluctant to do so.
The TARDIS has been taken within the walled city of Troy as a prize and is presented to King Priam by his son Paris, but Priam is unimpressed and more interested in getting revenge for the death of his son Hector. The blue police box is denounced by Priam’s daughter, the prophetess Cassandra, as dangerous - she has dreamt that the Greeks will leave a gift on the plain which will contain soldiers to attack the Trojans. She demands that the TARDIS be burnt and a pyre is constructed around it, but before it can be set alight, Vicki emerges from within the TARDIS and this is taken as a sign from the gods. The King and Paris are enchanted by her, dressed as she is in a wonderful gown, and the King renames her Cressida and makes her a favourite at court. This enrages Cassandra, who believes Vicki to be a rival prophet.
Priam sends Paris out on to the plains once more to avenge Hector. Paris calls for his rival Achilles to present himself, and Steven manages to persuade the Greeks to send him in Greek armor instead, hoping he can get himself injured and then taken prisoner to Troy to search for Vicki. Adopting the name Diomede, Steven engages Achilles in battle and his ruse works when Paris decides to take him as a prisoner back to the city. When he arrives Vicki greets him with his real name and this is taken by Cassandra as a sign they are both spies. She calls for soldiers to kill them both.
Paris intervenes to save Steven and Vicki, prompting Priam to ask Vicki to foretell how the war might be ended soon, as he is tired of conflict. Unless she helps him end the war, however, he warns she will die the following day. Steven and Vicki are taken to the cells to prompt her into prophecy. Whilst there Steven tells Vicki that the Doctor has a similar deadline to win the war for the Greeks. Cyclops appears near Steven’s cell and is given a message for the Doctor, asking him to avoid an attack for two days so that they are not killed for failing Troy. The next visitor to the cells is Priam’s youngest son, Troilus, who has formed a romantic attachment to “Cressida.” Vicki is equally attracted to him, and seems successful in persuading him to try to get them released. When Troilus departs, it seems that Vicki has indeed fallen for him, contemplating even staying in this time period indefinitely. Elsewhere, Cyclops is slain before he can pass on his message.
The Doctor has now come under such pressure to help the Greeks he eventually proposes the use of a wooden horse to Odysseus. The construction will be left on the plains outside Troy and filled with Greeks, who hope the horse will be taken within the city, allowing them to sneak out and attack the population. Agamemnon approves the plan, but it is also decided the Doctor will be placed inside the horse for its fateful journey. The Greeks build the horse during the night and the following morning the Doctor and Odysseus join the soldiers inside. Soon the gift is placed on the plains and, when day breaks, it is spotted by the Trojans and dragged with ropes inside their city.
The Trojans respond to the seeming disappearance of the Greek army by rejoicing, and Priam has Vicki released in thanks for her supposed good work. Steven, however, is kept in prison due to Troilus’ jealousy. When Vicki reaches the court, she learns from Paris that the wooden horse has been found on the plains and is being brought into the city. Priam interprets the Great Horse of Asia as a sign of their victory, brushing aside Cassandra’s worries. The gates of the city are open and the horse is now within.
The Trojans dismiss Cassandra’s prophecies (in the myths, Cassandra was given the gift of prophecy by Apollo, but then cursed never to be believed) but in the melee Vicki slips away and rescues Steven from the dungeons. They then head for the square, where a vast crowd has assembled to greet the giant wooden horse, and worry about what will happen when the Greeks hidden inside disembark. Cassandra’s handmaiden, Katarina, arrives in the square to find Vicki for her mistress. This prompts Vicki to leave Steven in a hiding place (his escape in Greek armour having now been noticed) while she mingles with the royal party that has just arrived. She then heads off to the palace where she meets Troilus and, aware of the carnage to come, she tries to persuade him to flee with her from the city by telling him Diomede, his rival, is on the plain. He is persuaded to venture outside.
Night falls again, and under the cover of darkness the Greek navy returns to the Trojan coast, while the Doctor, Odysseus and the Greek soldiers exit the horse. The city is soon besieged and the populace butchered by the Greeks. Priam, Paris, and the proven Cassandra are soon the prisoners of Odysseus. The two men are slain and Cassandra is kept alive as a prize for Agamemnon himself. She is taken away in bondage, prophesying Odysseus that he won't see home for another 10 years and death for his people. Out on the plain Troilus finds Achilles and, staggered that the Greek army is back again, engages Achilles and slays him, though he is wounded in the process.
The Doctor finds Vicki in the carnage and they hide in the TARDIS while Katarina, who has been trailing Vicki, obliges the Doctor by searching for Steven. She finds him in battle with a Trojan soldier and he is badly wounded, but she helps him return to the Doctor’s "blue temple". When Katarina and Steven reach it, both the Doctor and Vicki seem very tense. Odysseus arrives and the Doctor takes the opportunity to dematerialise the TARDIS with Steven and Katarina on board. Vicki, however, has slipped away with his blessing. She journeys on to the plains where she finds Troilus and they declare their love. Moments later Troilus’ cousin Aeneas arrives with reinforcements and helps them escape the area.
Aboard the TARDIS, the Doctor explains Vicki has departed with his blessing. He is very concerned that Steven’s wound is now infected and the situation is getting worse. Katarina believes they have already died and are now en route to the afterlife. The Doctor knows they need to secure the right medication to save Steven and hopes their next landing will provide it.