Asatruarfelagid was founded in Reykjavik in 1972 by a small group that included the farmer and poet Sveinbjorn Beinteinsson, and it was granted state recognition as a registered religious organisation the following year. That made Iceland the first modern state to give a heathen body the same legal standing as a church, with the right to conduct legally valid marriages and to receive the parish charge on behalf of its members. Sveinbjorn served as allsherjargodi, the presiding office, until his death, and he was widely known outside the organisation for his rimur chanting, a living Icelandic verse form he used for the old poetry.
The organisation has grown from a few dozen members to several thousand, which in a population the size of Iceland makes it one of the larger non Lutheran bodies in the country. Its public positions have been consistently liberal. It has conducted same sex marriages since they became legal in Iceland, and its leadership has been outspoken against the use of Norse symbols by the far right, which is a recurring problem for heathen groups internationally and one Asatruarfelagid has addressed directly rather than quietly.
A purpose built temple at Oskjuhlid in Reykjavik has been under construction since 2015 and has run many years past its intended completion. It would be the first structure of its kind built in Iceland in roughly a thousand years.
Two cautions are worth stating plainly. The organisation does not claim an unbroken line from the pre Christian period, and describes its practice as a modern one drawing on preserved sources. And the separate Icelandic tradition concerning huldufolk, the hidden people, is not part of it, whatever the tourist literature suggests.