With the lead warriors of both sides dead in the tenth year of the war, the Greeks had yet to make any impression on the city of Troy, whose walls stood as solid as they had been at the start.
As was customary, Achilles’ arms and armour were to be passed on to a successor. As they had been made specially for him by Hephaestus, they were particularly sought-after. Two contenders emerged, Ajax the Great and Odysseus. Agamemnon therefore summoned the leading Greek warriors to determine who was to be given Achilles’ unique arms and armour.
Ajax put his case first, claiming that, when Hector tried to set fire to the Greek fleet, it was he who had stayed to fight the Trojans, and that he’d even had to save Ulysses on the battlefield. He concluded by proposing that the two should settle the matter in a duel, to the delight of the other Greek warriors around them. For his part, Odysseus put an eloquent argument that it was he who had found Achilles hiding on the island of Skyros and brought him to the war. He had also killed a Trojan spy, Dolon, had been wounded in battle, and had later carried the dead body of Achilles from the battlefield.

Leonaert Bramer’s small painting on copper of The Quarrel between Ajax and Odysseus was made between about 1625-30. The pair stand in their armour, next to tents pitched at the foot of Troy’s mighty walls. At their feet is the armour of Achilles, and all around them are Greek warriors, some in exotic dress suggesting more distant origins.
Achilles’ arms and armour were awarded to Odysseus, causing Ajax to become mad. Before dawn the following morning, he set out with his sword to avenge his defeat. Athena convinced him that the Greeks’ livestock were his enemy, so he set about slaughtering them. Athena then restored his sanity, and Ajax was so distressed when he saw what he had done, that he killed himself immediately by throwing himself onto his sword.

Ajax’s suicide appears prominently in one of Nicolas Poussin’s greatest narrative paintings: The Empire of Flora, painted in early 1631. It’s set in a garden, with trees in the left background, a flower-laden system of pergolas, a large water feature, and dancing putti. In this are a series of well-known characters, one of whom is Ajax, shown in the act of falling on his sword, in the detail below.

With another of their leading warriors dead, the Greeks were in despair. They captured the Trojan soothsayer Helenos, who told them that they would never capture the city without their master-archer Philoctetes and his bow of Heracles, who had been abandoned on the island of Lemnos following his snake-bite. Helenos also said that Achilles’ son Neoptolemus had to be brought from Skyros, and the Greeks had to remove the sacred talisman the Palladium from the city.
Diomedes went to Lemnos and returned with Philoctetes and the bow of Heracles, while Odysseus fetched Neoptolemus. Once Philoctetes’ snake-bite had been healed, the archer took on Paris in combat, and his poisoned arrow sank deep into the Trojan’s flesh: he was dying.

Fearing his imminent death, Paris pleaded with his former wife Oenone to heal him. But, as shown in Léon Cogniet’s Oenone Refuses to Rescue Paris at the Siege of Troy from 1816, she refused and left him to return to Helen and die. Oenone was then overcome with remorse and threw herself onto his funeral pyre. Cogniet shows the dying Paris, surrounded by warrior colleagues and looking imploringly towards Oenone, her back turned on him as she walks away. At the right edge, wearing a golden crown, is her successor, Queen Helen.
When Odysseus returned with Neoptolemus, he handed him the arms and armour of the young warrior’s father Achilles, whose ghost visited his son to inspire him in battle. Shortly afterwards, Neoptolemus entered combat and killed a great many Trojans, including the much-feared Mysian (Hittite) warrior Eurypylos. After that death, the Trojans fled back into their city and wouldn’t venture outside its walls again.
Odysseus, probably inspired by Athena, then came up with the idea of constructing a wooden horse as a means of getting a team of their warriors inside the impregnable city. While carpenters were at work on that project, Odysseus entered the city in disguise and secretly told Helen of the plan to give Troy the horse. She agreed to signal the Greeks with a torch once the horse had been brought safely inside the city walls, so enabling those forces outside to launch their attack.
The remaining task of removing the Palladium required another night visit into the city, this time by Odysseus and Diomedes, who entered through its main sewer. They returned with the talisman, to find the wooden horse ready to deploy.
Once the team of a dozen or so Greeks led by Odysseus had got inside the body of the horse, it was moved to the shore in front of the city, and the rest of the Greek force burned their huts and sailed off, apparently leaving the horse as a peace offering. In fact they sailed only just out of sight, and waited.
The following morning, the Trojans discovered the Greeks had gone, so hauled the horse up and into the city, dismantling some of their defences to get it through the walls.

Lovis Corinth’s Trojan Horse from 1924 shows the horse still outside the city’s gate.

Tiepolo’s Procession of the Trojan Horse in Troy (1773) is one of his series showing the construction and entry of the horse into the city. He follows accounts that refer to Troy’s women and children hauling the structure using lines, and some reporting that it was ostensibly an apology for the theft of the Palladium.
The Trojans then went and drank and feasted what they had presumed to be their victory.

Henri-Paul Motte’s Trojan Horse from 1874 shows the Greek force as they leave the horse later that night, in their bid to seize control of the city from within.