From a reader: "should one consider the Iliad (and the Odyssey, too) as history or myth? The gods' participation was myth, but I also remember that an archeologist went looking for Troy and found it (however badly the excavations damaged the remains)."
Not to be too Clintonian about it, but this question depends on how you define the words "myth" and "history."
If "myth" = a fanciful story about the gods which explains natural phenomena (such as winter, spring, summer and fall), then the Iliad and Odyssey don't qualify.
If "history" = verifiable events recorded by faithful witnesses whose accounts mostly agree with one another, then the Iliad and Odyssey, again, don't qualify.
Neither definition contain any part of the word "true." That's because the ancient Greeks did not concern themselves with absolute truth. They were more interested in what was compelling, convincing, and true to their experience.
Ancient peoples believed that both the Iliad and the Odyssey happened a long time before the stories gained popularity. Is that history? It was in the ancient world. We cannot, however, reliably verify that what happened in these two epic poems actually happened. So for us, neither the Iliad nor the Odyssey can be considered history.
It's true that a banker named Heinrich Schliemann discovered and excavated Troy (and other cities from Greek Mythology), and that a TV show called In Search of the Trojan War found that there is an historical basis for Homer's poems. Archeologists continue the debate using physical evidence, and Bronze Age linguists have found letters with names which sound very similar to Ilium (an ancient name of Troy), Priam (the king of Troy), Alexander (another name for Paris, prince of Troy), a god with a name very much like Apollo, and foreign names that sound very much like Achaeans and Dardanians (that is, Greeks). So Homer may have been written the first historical novel. More scholarship could tell us a lot more.
In fact, I'd lay money that there was some kind of Trojan War. Our imaginations always use the real world in order to create stories. We could never have told a story about dragons if there had never been snakes. And who knows-- maybe there are dragons, too.