Islands Svefneyjar form the innermost part of the so-called Inneyjar Area comprising of Islands Hvallatur, Skaleyjar and Svidnur among more than 400 other islands and islets. The distance from Island Skjaldarey to Island Grisabol is 15½ km and 26 km between the outmost skerries on both sides. During the lowest tides most of the Svefneyjar Islands can be reached on foot. The Flatey Channel between Islands Inneyjar and Island Flatey is mostly free of skerries and opens into the northern part of the bay whereas its southern end faces the open sea. This channel is narrowest between Island Flatey and Islands Svefneyjar and is sometimes called the Svefneyja Channel.
The home island of Islands Svefneyjar is among the westernmost ones and the largest of Islands Inneyjar. It is about 1½ km long and ½ km wide and shelters eastern islands behind it against the ocean waves, or puts them to sleep, which is fitting for their names, The Sleep Islands. The main advantages of the islands are the eider colonies, seaweed, spring baby seals, egg picking and bird hunting. The cultivation possibilities of the home island are better than on most other islands and therefore conditions for traditional farming are good. The island yielded sufficient fodder for 30 cows. Shore grazings were rather hazardous, especially when the tide was at its lowest and the sheep had to be watched carefully to prevent them from drowning on the skerries, when the tide came in. When the Seaweed Factory at Reykholar started its operation, a new trade was born on Islands Svefneyjar. The people there were the first to start harvesting the seaweed around the islands.
The Book of Settlements mentions the salt making of chieftain Hallsteinn of Hallsteinsnes on the islands. He sent his slaves there for the purpose and once, when he came there to check on them he found them sleeping in a depression in the landscape. This incident is probably the reason for the name of the islands. According to the legend, he took the slaves to the Islands Svidnur, where he hanged them in a rift between two cliffs, which was called The Gallow (Galgi) afterwards. If there is any truth in these words, the islands were not inhabited until late during the Age of Settlements. The Sturlunga Saga mentions the islands, when one of the chieftains of the 13th century gives them to a good friend of his.
The parents of Eggert Olafsson, poet and one of the pioneers of the restoration of Iceland, lived there for a few years and their son was born on the home island. He drowned when crossing the bay on his honeymoon. The home fields and houses on the home island mostly date back to the 20th century. The concrete house was built in 1930. On the cliffs by the Baejarsund Channel is a sod hut, which is much older, the so-called Ranakofi. According to the mythology and common belief, it had to be maintained and must not collapse. When people had stopped believing in this superstition, they stopped maintaining it and it collapsed. The result was the drowning of Eggert Olafsson. Since then it has been maintained according to the legend.
Islands Svefneyjar have not been inhabited for quite a few years, but during summer the advantages of the islands are exploited.