Hjorleifshofdi is a freestanding, 221 m high hyaloclastite headland on the outwash plain Myrdalssandur. According to Book of Settlements, a bay reached the foothills of this low mountain, but was filled up by the constant flood waves connected with the Katla eruptions. Now the distance between the promontory and the sea is about 1½ mile.

In 874, the families, domestics and slaves of two foster brothers, Ingolfur and Hjorleifur, were on their way to Iceland to settle permanently. Their ships were separated in a storm and each family spent the next winter on separate promontories, which were consequently named after the aforementioned men. The next spring Hjorleifur's slaves attacked and killed him and his free men. They took the women to the ship and sailed to the Westman Islands to hide from Ingolfur, who found them and killed. The burial mound of Hjorleifur is said to be somewhere on his promontory, probably close to the highest point.

The first farms stood just west of the promontory until 1721, when and eruption of the volcano Katla caused a devastating flood, which swept away the houses and the green pastures and meadows. After that, the farms stood on the promontory itself. The last one was abandoned just before the middle of the 20th century. Up to the same time, men were roped down the precipices for birds (fulmar chicks), which were a part of the diet at the time and still are among the people, who stick to the old traditions.
Vik in Myrdal