Hallgrímskirkja, the tallest and largest church in Iceland, is Reykjavík's most photographed emblem by far, visible from everywhere in the capital. It was designed by state architect Guðjón Samúelsson (1887-1950), who never saw it completed: Work began in 1945 and continued 49 years. The church is named for Reverend Hallgrímur Pétursson (1614-1674), Iceland's foremost hymn writer, and also an ecclesiastical scholar and poet. His best-known work, Hymns of the Passion, is still sung and recited as verse in homes throughout Iceland (an English translation is available in the gift shop). For a fee you can ascend the 75m (246-ft.) steeple by elevator for great views over the city. At the top are three bells representing Hallgrímur, his wife, and his daughter who died young.

The distinctive exterior, with its prominent steeple, is often described in terms both primordial and futuristic—as if the church were some kind of volcano or glacier transformed into a rocket ship. Guðjón was indeed inspired by the Icelandic landscape, and the frontal columns are meant to resemble the hexagonal basalt formed by cooling lava. The interior is quite traditional in contrast, with its Gothic high-pointed vaults and tall, narrow windows. The uniform, textured-concrete surfaces can seem pedestrian, even to those accustomed to Lutheran principles of simplicity, and the altar is so ordinary as to resemble a hotel lobby. It could have been very different: a photograph hung in the entry hall depicts Einar Jónsson's proposed alternative design, a fantastical creation to rival Gaudí's cathedral in Barcelona. An Art Deco spire supports human figures in relief trudging upward amidst Middle Eastern-inspired domes.

Concerts here often involve the church's most popular interior feature: a gigantic organ built in Germany in 1992. It's about 50 feet tall, with 72 stops, 5,275 pipes, and remarkable sound projection. The church also hosts drama, art exhibitions, even public debates. Especially recommended are choral performances, a form in which Icelanders have always excelled.

A statue of Leifur (Leif) Eiríksson is aligned directly in front of the church, as if he's about to lead it down the hill. The statue was a gift from the U.S. to commemorate the 1,000th anniversary of the founding of Iceland's parliament. It was also a tacit acknowledgment that Leifur beat Christopher Columbus to North America by almost 500 years. (Excavations in Newfoundland have settled this question beyond a doubt.) He certainly strikes a heroic pose, but looks rather like a comic-book figure once you've seen the Viking statues in the Einar Jónsson museum next door.