To be more precise, it is referred to as Icelandic Krona or Kronur in its plural form, and is denoted as ISK. The currency symbol is kr. Coin denominations are available in 1, 5, 10, 50 and 100, while bank notes are comprised of 500, 1000, 2000 and 5000.
To acquaint yourself with using change in this currency, one Krona is composed of 100 aurar (like cents or pennies) but in reality, the 5, 10 and 50 coins have been pulled from circulation since 2003. It was decided in 2002 that all monetary amounts on Icelandic invoices and documents should indicate whole Kronur amounts only. The 5 aurar coin was considered to be the least valuable coin in circulation, as it equates to a mere 0.06 Euro cent. Since 2003, Icelandic banks no longer accept any coins denominated in aurar.
Krona directly translates to mean "crown" and is related to similar Scandinavian currencies. The ISK only became a separate currency from the Scandinavian Krona after Iceland gained independence from Denmark in 1918. The Central Bank of Iceland has controlled the circulation since 1961, and in 1980, the Krona was revalued. 100 old Kronur is now worth 1 new Krona.
Most hotels will exchange currency, but needless to you say, you will get a much better rate at a bank, as well as ATMs. As far as possible, avoid using other exchange offices; their commission rate can be as high as 9 % and are generally considered money traps for tourists.
Keep in mind that some tourist shops will accept both dollars and Euro, but for the sake of being money wise, it is best to carry Kronur on you. ATMs are scattered all over the cities, and MasterCard and VISA are widely accepted. Take note, though, that American Express will hardly get you anywhere in Iceland.
Regarding purchases, VAT is included in the price of your goods. Based on the average rule of thumb, if you spend over 4000 ISK in a shop, you can claim up to 15 % back on your purchase. The store will supply you with a tax refund form that needs to be submitted at the airport before your departure.
The Central Bank of Iceland, in its history of the Icelandic currency, states: "For more than thirty five years the Central Bank of Iceland has been responsible for the issue of all official currency in Iceland, both banknotes and coinage, at first by a special agreement with the Ministry of Finance in 1966, and then under the Currency Act of 1968. Prior to that, the Central Bank was responsible only for issuing banknotes, while coinage was under the auspices of the Treasury."
"The history of official currency in Iceland spans more than two hundred years, and the Central Bank feels it has a certain duty in this respect. The Central Bank and National Museum of Iceland have collaborated on cultivating this legacy by maintaining a special numismatic collection devoted to the preservation of domestic and foreign coins and notes and the history of Icelandic currency. The Numismatic Museum was established under a special agreement between these two bodies, endorsed by the Minister of Education and Culture in 1985."
(From "The Currency of Iceland – Issues and features of Icelandic notes and coins", published by the Numismatic Collection of The Central Bank and the National Museum of Iceland in October 2002). This booklet can be downloaded from the Central Bank of Iceland website here.