Munkathvera is a farm, a church site and a former manor in the Laugaland benefice in the Eyjafiord District. The estate was one of the best in the area and was mostly occupied by influential people. Among them was Einar Thveraeingur, who is mentioned in several of the Sagas. He probably had the first church built on the property. The descendant of the first settler of the Eyjafiord Area, Glumur the Slayer, a wise man, a good poet and a prominent personality, but also unfair and hard-headed.
The monastery was founded in 1155 and continued until 1550, when the Icelanders were reformed. Bishop Jon Arason was a frequent visitor there, when he was young and finished his clerical studies there. His monument stands where the monastery stood before. In 1429 the church and the monastery burned down. Two priests were killed and one monk was burned severely. The so-called Sturlungar-burial ground is in the old cemetery, where chieftain Sighvatur Sturluson and his sons who were killed in the Battle of Orlygsstadir lie buried.