The medieval Icelandic Commonwealth (930-1262), having no central executive powers, did not apply capital punishment. It was, however, possible for the Althing to declare a man réttdræpur (English: "rightfully killable"). This made the killing of the person in question legal—although the executive power was invested in whosoever cared to pursue it, instead of being the duty of state officials.
According to a plaque at Thingvellir National Park, 72 people are known to have been executed in the period from 1602 to 1750. Execution methods included beheading, hanging, burning at the stake and drowning.
Later, when Iceland fell under the Danish Crown, Danish laws more or less applied. The frequency of capital punishment increased considerably with the adoption of Lutheranism in the 17th century, but gradually disappeared by the mid-19th century.
WHAT COULD THESE TWO POSSIBLE TALK ABOUT AT THE DINNER TABLE!?!?!?!