Odysseus' travels aren't historical, and the places shown in the adventures in the Odyssey are very heavily altered with fictional elements. But there was a strong tradition in antiquity of linking these adventures to real places. I'll call this process, the effort to link Odysseus' adventures to real places, 'localisation'.

It is perfectly possible that many localisations were already understood in Homer's epic. I say 'possible': in fact I think it rather likely. Greeks were actively colonising southern Italy and trading with the native Tyrrhenians at the time when the Odyssey was composed. Odysseus' adventures are a way of creating a prehistory for that region, making Odysseus programmatic for contemporary colonists. So the Italian parts of the Odyssey's geography are some of the most important.

The main localisations relate to three bundles of episodes:

• mainland Greece and Thrace: Telemachos' journey to Pylos and Sparta; Odysseus' visit to Ismaros and attack on the Kikones.
• Italy and Sicily: the island of the Kyklopes; Aiolos; the Laistrygonians; Kirke; speaking with the dead; the Sirens; Skylla and Charybdis; the cattle of the Sun.
• Kerkyra: Scheria, the land of the Phaiakes.

Two episodes were considered to be set elsewhere, but there is more disagreement among ancient sources as to where:

• the Lotos-eaters: generally imagined as being in northern Africa, sometimes in Libya, sometimes in Tunisia.
• Kalypso: sometimes imagined as being in Malta, sometimes in the Atlantic.

The Italian/Sicilian setting is the most elaborate: as I mentioned, Odysseus' adventures there are a way of creating a legendary prehistory for real colonists of Homer's time. The Kyklopes and Laistrygonians were normally imagined as being in Sicily, Aiolos at the Isole Eolie just to the north of Sicily, Kirke at Monte Circeo in Lazio, the consultation of the dead at Avernus and/or Cumae near Naples, the Sirens at the Sirenuse islets south of Sorrento, and Skylla and Charybdis at the Strait of Messina. There's very little disagreement in ancient sources about these, and some of them -- Kirke and the consultation of the dead -- correspond well with other things that we know about those places. The Romans founded a colony named after Kirke, Circeii, in the Archaic period, and Lake Avernus in Campania appears to have been an Italian counterpart to Acheron/Acherousia in Greece, where people could visit the lake and consult the spirits of the dead with the aid of priests called psychagogoi. A lost play by Aischylos, the Psychagogoi, may well have been set at Avernus too.

Kerkyra is almost always identified as the home of the Phaiakes in classical-era sources (e.g. Thucydides), but I'm a bit more doubtful whether this localisation was part of the geography that fed into the Odyssey. It seems too nearby, and too familiar, to be as outlandish as it is in Homer. Then again, Homer doesn't seem to have known the geography of the Ionian islands very well, so maybe Kerkyra wasn't as familiar as all that.

While some of Odysseus' adventures were imagined as happening in real places, that doesn't mean that the adventures themselves were imagined as real. Greek colonists in eastern Sicily didn't see Kyklopes wandering around, and settlers further north presumably knew that Monte Circeo (traditionally Kirke's home) wasn't an island. We're talking about an invented fictional past, superimposed on a partly imaginary geography.

So it's a matter of emphasis whether you regard the geography as real or fictional. Eratosthenes, for one, regarded it as fictional, and famously declared that 'You will find the setting of Odysseus' adventures when you find the cobbler who sewed up the bag of winds.' That hasn't stopped plenty of modern people from attempting their own localisations. In antiquity, too, Strabo took the opposite position, that everything was imagined as being in a real place, and that a geographer's job was to puzzle out which was which.

I'm trying to argue for a middle course here. Some bits of the geography are more real than others; but even the bits that are real are imaginary. They're real settings thrown back into an imaginary past.

Sicily is the island of the Kyklopes only in the sense that Ukraine is the setting of Conan the Barbarian. That is to say, it isn't. But it still provides some hooks for a storyteller to hang the story on.