[2] Harpa was designed by the Danish firm Henning Larsen Architects in co-operation with Danish-Icelandic artist Olafur Eliasson.

[3][4] The building was part of a redevelopment of the Austurhöfn area dubbed World Trade Center Reykjavík, which was temporarily abandoned when the 2008 Icelandic financial crisis took hold.

The development included a 400-room hotel, luxury apartments, retail units, restaurants, a car park and the new headquarters of Icelandic bank Landsbanki.

[2] The completion of the structure was uncertain until the government decided in 2008 to fully fund the rest of the construction costs for the half-built concert hall.

The Reykjavik Edition Hotel, managed by Marriott International opened in 2021 along with retail and restaurant units; Landsbankinn moved into their new headquarter building in early 2023.

This was the first time the façade was set to other uses than playing videos, and PONG was shown again the following year as a part of the Sónar Reykjavík festival.

[21] The European Film awards, Iceland Airwaves, Reykjavik Arts Festival and EVE fanfest have been hosted at Harpa.

[22] In its unfinished state, Harpa (under the earlier name Tónlistarhús) appears in the 2009 novel Gæska: Skáldsaga by Eiríkur Örn Norðdahl, where it is temporarily turned into a mosque in Reykjavík with the addition of a minaret.