Legend has it that Odysseus took shelter in one of Mljet's caves after a shipwreck, and the name's stuck ever since. You'll take a boat trip out from Pomena to take a look, and swim if you like, inside this egg-shaped cave.
Once Odysseus landed on the shores of Ogygia, now known as the island of Mljet, he couldn't resist the charm of the nymph Calypso and the island itself. So, it's said he stayed for seven years before he was free to go, and you'll see it all for yourself on this boat trip to Odysseus Cave.
After sailing for just over an hour, you'll anchor up in front of the cave, which from the outside looks just like a small tunnel carved into the limestone rock. Then it's up to you whether you swim or take a smaller boat inside, where once you're through to the other side, everything opens up before you. You'll have about an hour to take it all in before your return boat trip.