There has been some talk in Iceland about the non-extradition of two Polish nationals arrested in Poland for robbing a store in downtown Reykjavik. Here’s some an article about it: http://grapevine.is/Home/ReadArticle/Watch-Thief-Accomplices-Will-Not-Be-Extradited. This has pointed the attention of the public to the state extradition treaties with other countries. As of now, Iceland is not yet a part of European Arrest Warrant meaning that the situation is as follows. Most of the countries in Europe will not extradite its own citizens to Iceland and vice-versa. There is however a pan-nordic treaty en force, which goes further, allowing extradition of Icelanders to other Nordic countries and vice-versa. Additionally, Iceland has signed bilateral treaties on extradition with some European countries. These are also shown on the map, but they also do generally not facilitate for extradition of the country’s own-nationals.
Thus generally, Icelanders can be extradited to the Nordic countries, but not other European countries. Also a non-nordic Citizen can escape extradition to Iceland by staying in his home country.