Valley Geithellnar and the ancient manor Geithellar were named after a cave near the present farm Geithellnar.  According to the Book of Settlements, the two foster brothers, Ingolfur Arnarson and Hjorleifur Hrodmarsson, who were the first Norwegians to arrive to settle in Iceland, probably spent the winter of their reconnaissance trip in the valley before deciding on bringing their families along.  The valley is long and deep and penetrates the highlands to the east and northeast of the icecap Vatnajokull.  It is well vegetated in places and was densely populated in the past.

River Geithellnar receives most of its water from the small glacier Thrandarjokull.  A former course of the river, called Hraun, is a gorge containing the small lake Trollatjorn.  It was rich in brown trout and lake char in the past.

Once a poacher was attacked there by a monster and barely escaped.  He cast a spell on the lake and since then no fish has been caught there.  The course of River Geithellnaa is decorated with waterfalls and canyons, where it squeezes through narrows between hard dykes.