Liquor is sold in special stores, called Vínbúð (Vinbud) or “Ríkið” (the government). Why it is called by locals “Ríkið” is because these liquor stores are run by the government. There are many liquor stores around the country. Many travelers do not know about opening hours of these liquor stores. You can find information about them following this link.
The only way to buy liquor, if we do not talk about restaurants, is in these liquor stores. Note that the liquor stores are closed at Sundays, and other opening hours vary from town to town. It is not possible to buy liquor in other stores in Iceland. In grocery stores you can by light beer (pilsner), which is only 2,2% alcohol.
In the year 1915, alcohol was banned in Iceland. In 1922 wine was allowed. In 1935 alcohol was allowed, except beer. In the year 1989 beer was also allowed in Iceland.
When this is written in 2018, no alcohol is sold in other stores than Vinbud. For many years people have been arguing about if we should sell alcohol in supermarkets. Some parties at the parliament are trying to change this tradition/law to only sell alcohol only in government run liquor stores. What happens, only time will tell.
Alcohol consumption is only allowed to people from 20 years old and above. It is strictly forbidden to drink and drive. There is zero tolerance regarding that by law.
By law in Iceland it is forbidden to advertise alcohol.