[1] Known for its distinctively curved spire and side wings, it has been described as having become an important symbol for Iceland's national identity since its completion in 1986.

[2] The church is named after the Icelandic poet and cleric Hallgrímur Pétursson (1614–1674), author of the Passion Hymns.

He is said to have designed it to resemble the trap rocks, mountains and glaciers of Iceland's landscape,[4][5] in particular its columnar basalt "organ pipe" formations (such as those at Svartifoss).

[2] Architecturally, Hallgrímskirkja consists of three parts: The tower with the distinctly curved side wings which house service facilities, a nave in more traditional architecture, and a sanctuary at the other end of the nave, whose cylindrical shape has been described as evoking Viking war helmets.

Hallgrímskirkja is best described as a piece of Expressionist architecture because of its tower-like exterior, its rejection of traditional styles and its dynamic design.

[10] The statue of explorer Leif Erikson (c.970 – c.1020) by Alexander Stirling Calder in front of the church predates its construction.

It was a gift from the United States in honor of the 1930 Althing Millennial Festival, commemorating the 1000th anniversary of the convening of Iceland's parliament at Þingvellir in 930 AD.