This is the largest island off the east coast of Iceland, about 2 kmē in area, and the only populated one until a few decades ago. There was only one farm there and a church built in 1902. The highest lying point of the island, Hellisbjarg, is only 58 m high. The island is well vegetated, uneven and boggy. The cliffs abound in seafowl and a great number of eider ducks occupies the island during the breeding season.
There are several smaller islands around the main island, and two of them are connected with it by cable carriers. The lighthouse was built in 1922. Presumably the island was inhabited by Irish monks, when the Nordic settlement of Iceland started. They were called "papar", hence the name of the island.

Some pieces of small, wooden crucifixes were discovered there in 1927 and there are signs of ancient ruins, which have not been excavated yet. In 1972 archaeologist Kristian Eldjarn excavated a 10th century farm, a dwelling and a cow shed. The island offered quite a few advantages in the past and some of the farmers grew rich. The houses on the island have been maintained by the family, who lived there last, and used during summer.

There are two natural harbours In Papey. The main port is Selavogur in the west and Attaeringsvogur (Attaeringsvogur) in the north-west. Not too far on the northern part of the island, behind the farm Bjarg is a hill which is considered the church of the hidden people and above the harbour, Arhofn, on the western side of the island, is an impressive rock called Kastali (The Castle). There the hidden people reside. The lighthouse on the highest point was built in 1922.

Interesting boat trips to the island are on offer from Djupivogur.