Hallgrímskirkja (Church of Hallgrímur)
Reykjavik's highest and most imposing structure, Hallgrímskirkja, is visible from over 20km (12 miles) away. Begun in the late 1940s and completed in 1986, with its stark, light-filled interior and architectural resemblance to basaltic lava, it elicits mixed reactions. Most people visit it for the chance to view the city from the tower: the panorama is superb.

Skólavörðuholti
Tel: 510 1000.
Website: www.hallgrimskirkja.is (Icelandic only)
Free admission (church); charge for the tower.

Perlan (The Pearl)
A walk through landscaped gardens (including an artificial geyser) leads to the top of Öskjuhlíd Hill and Reykjavik's architectural masterpiece - the Pearl. This magnificent glass structure, which houses a revolving restaurant perched atop hot water tanks, is an engineering feat. The fourth level has an outside viewing deck offering views of the city, as it sprawls out below. On the ground floor is the Saga Museum, a multi-dimensional display depicting key moments in Icelandic history, and giving a compelling insight into how Icelanders lived from the settlement of the island at the end of the 9th century through to the Reformation period. The dioramas use eerily realistic silicone rubber figures, whose features were borrowed from Reykjavik residents, so don't be surprised if you recognise a familiar face on the streets of the capital.

Öskjuhlíd Hill
Tel: 562 0200.
Website: www.perlan.is   
Free admission.

Saga Museum
Tel: 511 1517 or 694 3096.
Website: www.sagamuseum.is 
Admission charge.

Listasafn Íslands (National Gallery of Iceland)
Iceland's National Gallery houses a permanent collection of paintings and sculpture by Icelandic and international artists from the 19th and 20th centuries. It also stages temporary exhibitions of Icelandic art. Housed in a modernist building that was originally built for ice storage, it comprises four exhibition rooms, a cafe, lecture hall, art library and bookshop.

Fríkirkjuvegur 7
Tel: 515 9600.
Website: www.listasafn.is 
Free admission.

Listasafn Reykjavikur (Reykjavik Art Museum)
Known collectively as the Reykjavik Art Museum and housed in three locations around the city (Harbour House or Hafnarhúsid, Ásmundur Sveinsson Sculpture Museum and the Kjarval Collection) the museum offers up a wealth of Icelandic culture. The Harbour House lays claim to the Erró Collection, the Architectural Museum and the Reykjavik Art Collection. Located near the harbour, as its name indicates, the building also boasts six exhibition halls, a multi-purpose space, an outdoor courtyard, bookshop and cafe. It houses changing exhibitions of work by modern Icelandic and international artists in a variety of media. Dedicated to the sculptures and drawings of Ásmundur Sveinsson, the Ásmundur Sveinsson Sculpture Museum collection is housed in the artist's former home and studio. The Kjarvalsstadethir gallery houses works by leading Icelandic and international artists of the 20th century. The gallery has a shop and a cafe overlooking the Miklatún Park and the Perlan.

Website: www.listasafnreykjavikur.is
Admission charge (daily ticket to all three museums); free Mon.

Harbour House
Tryggvagötu 17
Tel: 590 1200. 

Ásmundur Sveinsson Sculpture Museum
Sigtún
Tel: 553 2155.

Kjarvalsstadethir
Flókagata
Tel: 517 1290.

Árbæjarsafn (Árbær Open-Air Folk Museum)
Árbæjarsafn is Reykjavík's folk museum, and the largest open-air museum in Iceland. It comprises about 30 buildings, most of them brought to the museum site from downtown Reykjavík. They date from the period 1820-1920. In the houses, reconstructions of homes and workshops and special exhibitions may be seen. Events are scheduled every Sunday, with live accordion music. Craftspeople demonstrate traditional tasks almost every day in the museum. Milking takes place at 1630 every day and is always a popular event with children. There are also children's horse rides on Saturdays.

Árbæjarsafn v/Kistuhyl
Tel: 411 6300.
Website: www.arbaejarsafn.is
Admission charge.

Thjódminjasafn Íslands (National Museum)
Founded in 1863, the National Museum has a huge range of relics and tools spanning Reykjavik's 11 centuries of history. It houses everything from medieval altar cloths through to its star attraction - a 12th-century door depicting a Norse battle scene. The museum covers all aspects of Icelandic life, from the time of the settlements to the present day. Featured at the museum are archaeological finds buried in the eruption at Mount Hekla in 1106, the first bible printed in Icelandic, a history of Icelandic witchcraft, and items such as the census of 1703, with detailed accounts of people and livestock across Iceland.

Sudurgata 41
Tel: 530 2200.
Website: www.natmus.is 
Admission charge, free Wed. Guided tours available.

Heita Potturinn (Hot Pots)
Geothermal swimming pools and hot pots play a major part in Icelandic life as swimming lessons are mandatory and students cannot graduate without passing a swimming test. The hottest pools have controlled temperatures of up to 44°C (108°F) and are said to have certain medical benefits. As the pools are not heavily chlorinated, it is compulsory to take a nude shower and wash thoroughly before entering. The largest is Laugardalslaug, which has a 50m (150ft) pool, curved waterslide, five hot pots of differing temperatures and a steam bath. Many locals pop in between 0800 and 0900 to relax before work and catch up on the gossip, making it a good time for curious visitors to join in. If you are planning on spending a few days in Reykjavik, it is possible to purchase a 10-visit season ticket, which is valid for all the city pools.

Laugardalur, Sundlaugavegur
Tel: 553 4039.
Website: www.spacity.is
Admission charge.