In the Middle Ages, approximately 100 years after the settlement of Iceland in the 9th century, the vast majority of Icelanders was mostly worshipping the Norse gods such as Óðinn, Þór and Freyja.
Some settlers, however, were of Christian faith, originating from Viking settlements in Ireland, England and Scotland.

One cannot exactly tell how and when the medieval Icelanders abandoned their pagan belief in favour of Christianity so one has to rely on a few written sources.
The most extensive sources mentioning these events are the Book of the Icelanders by Ari Þorgilsson, the Icelandic family sagas and Church chronicles about the first preachers and bishops.
Þorgilsson's accounts of the events surrounding the conversion are widely considered as being reliable.
Several missionaries had visited Iceland from 980 AD onwards but were mostly ignored by the pagan islanders.
Among these first Christian preachers was an Icelander returning from abroad, a man called Þorvaldur Konráðsson, who travelled in the company of a Saxon priest called Friedrich.
Þorvaldur and Friedrich had some success, especially in the North, but they had to flee the country when Þorvaldur killed men during their travels.
When Norwegian Viking Ólafur Tryggvason became King of Norway in 995 AD, he converted to Christianity and he was determined to establish his faith in all of the Nordic countries and didn't hesitate to use violence or shed blood to achieve his goal.
Therefore King Ólafur I sent out missionary priests to intensify the efforts to spread his religion.

One of the first priest was an Icelander named Stefnir Þorgilsson, who began attacking and breaking down heathen temples. This acts of vandalism resulted with Stefnir being outlawed and expelled from Iceland.
All the missionary priests coming to Iceland had only very limited success in their attempts to convert Icelanders as they were ridiculed and eventually forced to flee the country.
Being displeased with this failures, King Ólafur sent his flemish bishop Þangbrandur to Iceland in 999 AD to spread the word of the Lord.
Þangbrandur met a similar fate as his predecessors. In the beginning, he boasted some success in baptising a few noble chieftains but he also ran into opposition and even killed a few Icelandic skalds who composed lampooning poetry about him.
The Alþingi, the Icelandic parliament, finally outlawed bishop Þangbrandur who then returned to Norway. He complained about the Icelanders and told his king that he had little hope that the country could ever be converted.
In hearing that, King Ólafur I got so furious that he threatened to kill every pagan Icelander in Norway.
Two of the Icelandic chieftains Þangbrandur had converted to Christianity, Gissur hvíti (“the White”) and his son in law Hjalti Skeggjason, sought an audience with the king and persuaded him out of his vendetta by explaining that the previous attempts to convert Icelanders had only failed because the missionary priests had proceeded with violence and murders.
They promised the king to spread Christianity by preaching the religion instead of using force. Of course they wanted their own faith to be established among their countrymen, but they also did this for the greater good of Iceland as it was vital to have good relations to Norway.
Not even one year later, in 1000 AD, the king died in battle. By then about half the Icelandic population had become Christian, and the issue of religion caused harsh disputes at parliament.

The Christian and pagan fractions didn't want to share the same laws and the Christian Icelanders even chose a new law speaker, Sídu-Hallur Þórsteinsson.
Although both parties were very eager to win the dispute, they desired above all to preserve peace and unity in the country.
The chieftains chose one law speaker named Þorgeir Þorkelsson who should come up with a compromise acceptable to everyone. Þorgeir, a heathen and so called goði, a chieftain that also held a religious office, was also referred to as Ljósvetningagoði (“The Goði of the bright lake”).
After a day and night of silent meditation, Þorgeir gave a famous speech in front of a huge audience at the parliament site, avoiding a potentially disastrous civil conflict. He decided that the only way to maintain peace in Iceland was to have only one religion and this ought to be Christianity.

Furthermore, he decreed that everyone not already baptised must convert to the new faith. In the law, three exceptions were made to benefit the pagans:
1. The old laws allowing the exposure of newborn children would remain in force.
2. Eating horsemeat would still be allowed.
3. People could continue to make pagan sacrifices and worship the old gods but in private.

Þorgeir Ljósvetningagoði's speech marked a turning point in Iceland and Christianity started to make its way into Icelandic society without anyone having to resort to weapons or bloodshed.
Although certainly not everybody was pleased about this verdict, the people of Iceland accepted the new law of the land and obeyed Þorgeir's arbitration.

According to legend, Þorgeir gathered all the statues of the old heathen deities at his homestead and threw them in a nearby waterfall which is since then called Goðafoss (“Waterfall of the Gods”).

Civil war was averted via arbitration and Iceland's peaceful conversion to Christianity is in many ways remarkable, given the decades of civil strife and bloodshed in other countries caused by religious disputes.
A likely explanation is that medieval Icelanders were rather to accept religious change than a civil war.
Once the Christian church was firmly in control in Iceland, the consumption of horse meat, infanticide, and pagan rituals practiced in private were banned.

Almost 1000 years later, Icelanders began to turn back towards the old religion. In the 1970s, the so called Ásatrúarfélagið (“Ásatrú Association”) was founded, Ásatrú meaning the faith in the old Norse gods, the Æsir. In the past decade the neo-pagan organisation has gathered quite some popularity and counts 2093 members as of October 2012.
The Ásatrúarfélagið does not have a fixed religious dogma or theology but the high priests have tended towards a pantheistic worldview. The central ritual is the communal blót feast, the traditional sacrifice to the Norse gods and the spirits of the land. But the priests or goðar also conduct name-giving ceremonies, weddings and funerals etc.
So after all, it seems as if the Icelanders are slowly rediscovering their ancestors` beliefs and customs.