Höfði is a house in northern Reykjavík, the capital city of Iceland, built in 1909. Höfði is located at Félagstún. Initially, it was built for the French consul Jean-Paul Brillouin in Iceland and was the exclusive residence of poet and businessman Einar Benediktsson (1864-1940) for many years. It is best known as the location for the 1986 Reykjavík Summit meeting of presidents Ronald Reagan of the United States and Mikhail Gorbachev of the Union of Soviet Socialist Republics. That effectively was a step to the end of the Cold War. Within the building the flags of the USA and the USSR are cross-hung to commemorate the meeting.
The city of Reykjavík purchased the house in 1958, restored it to its former glory. From that time used it for formal receptions and festive occasions.
On 25 September 2009, on the building´s 100th birthday, Höfði was damaged in a fire. All irreplaceable artifacts were saved.

The memoirs of one of the earliest occupants of Höfði state that the house is inhabited by the spirit of a young woman. Accounts vary on who she is but most commonly she is either a suicide or drowning victim. John Greenway, who inhabited the house in 1952, insisted that it be sold and the British consulate moved elsewhere, because of what he called ´bumps in the night´. He even applied for special permission from the Foreign Office to do so. That same year the house was sold back to the Icelandic government.
Popular local legends differ from the accounts of the house´s inhabitants; the most popular of which is that the house is a Viking burial site. For this reason locals say the liquor cabinet of the house is frequently raided by spirits.
The legend has even gained recognition by the Foreign Ministry who have officially stated that "We do not confirm or deny that the Hofdi has a ghost."