I have heard many things...
There are many locals who take great delight in shoving things like fermented shark and pickled ram's testicles in your face boldly claiming that this is traditional Icelandic food.And go for it if you have the stomach and you might even be surprised, but keep in mind these claims are only partly true.
Remember that for centuries Iceland was a very poor and remote country fighting for survival through harsh winters, cold summers, earthquakes and volcanic eruptions. People lived of fishing and farming and used whatever means necessary to preserve their food.There are the traditional ways of curing and smoking and then the slightly more unorthodox way of preserving sheep products in whey.
However, in terms of what is traditional and what not most locals will talk about a leg of lamb with gravy as their Sunday roast or boiled haddock and potatoes with melted butter as Tuesday fish. Of course things have been changing here in the last decades same as anywhere else, so we could add Friday pizza and Saturday sushi to this list,although neither wheat nor rice is grown in Iceland.
The Icelandic lamb is the undisputed crown jewel of farming here. Traditionally raised grazing the highlands with their mothers through the summer giving the meat a distinct flavour of arctic herbs, clean water and midnight sun. Most restaurants in Iceland will serve lamb in some form and it can be highly recommended, whether cured or smoked as a starter, or roasted or grilled as main course, it is a must to try while in Iceland.
Another thing to be on the lookout for are dairy products. Cattle in Iceland have been bread for centuries with more focus on milk production than meat. The Icelandic butter of course is amazing, but also try various other products such as cheese, yogurt and the local skyr.
There is not much but during the short hunting seasons in the fall and up until Christmas there is a chance to try geese, ptarmigans and caribou which all have a distinct local flavors from their died of berries and arctic herbs. If you have a chance to go to a game buffet, specially if you are located in east Iceland, take the opportunity. There are also the mushrooms from the birch forests, arctic blueberries, crow-berries and rhubarb, and the small crops people manage from the short summers.
Then there is the magnificent life beneath the surface of almost every lake, river and stream in Iceland. Salmon, trout and arctic char. These are also a must, find out if what they have on the menu is from local anglers and enjoy a great treat from nature's buffet. Whether grilled, smoked or cured these fresh water fish are delicacy. And then there is the wealth of the Sea.
Yes! Some of the richest fishing grounds of the North Atlantic are just off the Icelandic coastline. Try any of the amazing variety of fish cought in these waters, cod, haddock,halibut, monkfish, wolffish and flounder. There are also other seadwellers such as langoustines, crabs, prawns and various types of shells witch will not disappoint. There are various restaurants offering all kinds of seafood and because of all this fresh saltwater bounty sushi has become quite popular in the last few years, and basically anything from fish and chips to pots of mussels and continental towers of ocean treasures. It is well worth asking around or going on line and getting recommendations for the best places to enjoy any variation of the vibrant culinary culture blooming in Iceland.