The house was built in 1945 by Halldór and his wife Auður Sveinsdóttir. The architect was Ágúst Pálsson and the interior designer was Birta Fróðadóttir. Gljúfrasteinn is built on the banks of the river Kaldakvísl and is situated close to Laxness’s childhood home, Laxnes.
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Paintings by some of the most celebrated 20th century Icelandic artists adorn the walls of Gljúfrasteinn. Visitors can view works by artists such as Svavar Guðnason, Nína Tryggvadóttir, Louisa Matthíasdóttir, Jóhannes Kjarval, Karl Kvaran, Ásmundur Sveinsson, as well as works by the Danish painter Asger Jorn and the Norwegian painter Jakob Weidemann.
In 2002 Laxness's widow, Auður, sold the house to the Icelandic state. In September 2004 it was opened for the public as a museum. Visitors can take a guided tour through the house, and the museum hosts concerts during the summer.