So when we were in Naxos there were octopi hanging out to dry? near the port. But on that trip when we looked at the menus (and now reading on another site) it says the calamari served is usually frozen from California! Please explain Do they serve fresh octopus that has been marinated and slow cooked?

Calamari is squid, not octopus. Some restaurants will always choose to serve fresh seafood over frozen when fresh is available. Some won't bother or won't have access to fresh. It just depends.

Calamari isn't octopus. It's squid. I've eaten all kinds of octopus - fresh, grilled, in salads - all over Mediterranean countries. It's delicious. And I highly doubt any of it came from California - that would be a long, expensive trip.

Seafood you will encounter that has been frozen include calamari and swordfish. Go to the port early in the morning and you will see fishermen tenderising the octopus they caught that day. Octopus is plentiful in the Cyclades, so there is no need to import it frozen. Other fresh fish are scarce, hence the high prices.

OK got that now - octopus is NOT calamari. We had several wonderful meals of whole grilled fish - it was delicious and I don't remember it being too pricey (we were on Naxos) - could it have been frozen???

Why would it have been frozen? That would be beyond weird.

I asked that because Heimdall mentioned fresh fish was scarce and high priced

Certain fish, such as bream, red mullet & porgie are likely fresh ... but Salmon, Swordfish, Tuna, sole all are certain to be frozen. This is because the Med/Aegean waters are largely "fished out" (i.e. the traditional fish stocks were so heavily harvested they have never recovered). This is a legacy of WW II starvation & hardship ... at the end of that war, all the populations around those seas -- not just Greece but France, Spain, Turkey, African countries -- were impoverished and hungry, their farms were in ruins, so they turned to the sea. Leftover wartime munitions made it easy to "explode" the waters & fill a boat with the fish ... which nourished the hungry people, but damaged the fish stock until the various governments passed laws to stop the practice. Fishermen today mainly catch smaller species like sardines and smelt, and seafood like shrimp, squid, octopus etc.

Suec1, go to the display case in the taverna, and you will see the fresh fish still with their heads, tails, fins, etc, making it easier to tell how fresh it is. These will be the species of fish present in local waters, and chances are they will have been caught earlier that day. Fresh fish is normally sold by the kilo, and the fish you choose will be weighed to determine the price. If the fish has a fixed price on the menu, or if it has been cut into pieces, then it will probably have been thawed from frozen.