The Trojan War was the ten year war between the Trojans and the Greeks that caused these men to begin their journey.
Scylla and Charybdis
Odysseus and his men decide to stop at an island and steal from the cyclops that is living on it. They get caught by the cyclops and he eats several of Odysseus's men. Odysseus is able to trick the cyclops into getting drunk and sneaks out of his cave on the bellies of rams. After they escape to the ship Odysseus tells the cyclops what his name is, and the cyclops asks his father, Poseidon, to curse Odysseus's voyage.
Odysseus goes to Aeolia to ask him to give him all the winds except for the one that would blow him home. After Odysseus returns with the bag of wind his crew opens the bag and releases all of the winds.
Odysseus has to choose between facing Scylla and losing six men or going past Charybdis and him and all of his men dying. He decides to face Scylla and loses six of his men.
The men stop at Helio's island, and they are accompanied by Helio's sun cows. The men were warned by Tireias not to harm the cows, but when Odysseus leaves his crew kills the cows. When Helio sees this he threatens to take away the sun.
Odysseus finally arrives home with none of his men and many strangers in his home trying to court his wife.