Achilles didn't want to fight in the Trojan War, so he disguised himself as a girl in the court of Lycomedes, the King of Scyros. During that time, he had an affair with the princess, Deidamea, who gave birth to Neoptolemus.
Ten years later in the war, after the death of Achilles and Ajax the great and no signs of victory for the Greeks, the Greeks desperately captured the Trojan seer, Helenus, and forced him to tell them under what conditions could they take Troy. Helenus revealed to them that they could defeat Troy if they could acquire the poisonous arrows of Heracles (then in Philoctetes' possession); steal the Palladium (which led to the building of the famous wooden horse of Troy); and persuade Achilles' son to join the war. The Greeks made haste to fetch Neoptolemus at Scyros, and brought him to Troy.
Odysseus and Neoptolemus then went to Lemnos to retrieve Philoctetes. On the way to Troy, ten years earlier, Philoctetes was bitten by a snake on Chryse. Odysseus advised that he be left behind because the wound was festering and smelled bad. This retrieval is the plot of Philoctetes, a play by Sophocles.
In contrast to Achilles, a noble warrior who had shown mercy to Priam, Neoptolemus was savage and cruel. He killed Priam, Eurypylus, Polites and Astyanax, among others, and enslaved Helenus and Andromache after the war. The ghost of Achilles appeared to the survivors of the war, demanding Polyxena, the Trojan princess, be sacrificed before anybody could leave. Neoptolemus did so.
With Andromache, Helenus and Phoenix, Neoptolemus sailed to the Epirot Islands and then became the king of Epirus. With Andromache, Neoptolemus fathered Molossus, the ancestor of Olympias, mother of Alexander the Great.
Neoptolemus was killed after he attempted to take Hermione from Orestes as her father, Menelaus, promised, or after he denounced Apollo, the murderer of his father. He was killed by Orestes or some Delphian priests of Apollo.