Iceland's capital is unlike any other European city. Not only is Reykjavík ('smoky bay') the world's northernmost capital, it's also one of the newest, having established itself only in the late 19th century. Despite its name, it is now known as the 'smokeless city' thanks to its incessant winds and reliance on geothermal heat. Reykjavík boasts all the trappings of a modern European city as well as an interesting old town, white-washed wooden buildings, and rows of brightly painted concrete houses. Nearly everything of interest is within walking distance of the old settlement.

The Old Town, the city's hub, is a rustic area of grassy parks, lakes, markets and museums. Anyone remotely interested in Norse and Icelandic culture should head for the National Museum, which houses exhibits of religious and folk relics, and tools dating from the period of Settlement. The most renowned is a church door, carved around 1200, which depicts a Norse battle scene, while residing in the basement are nautical and agricultural tools and models of early fishing boats and ingenious farm implements. Immediately behind the museum is the Árni Magnússon Institute, a must-see for Saga buffs. The building contains a famous collection of works, including the Landnámabók and Njáls Saga, which were returned from Denmark to independent Iceland.

Modern Reykjavík sprawls eastward from the Old Town, and features several worthwhile attractions such as Hallgrímskirkja, an imposing church designed to resemble a mountain of lava. Although the word 'tacky' may spring to mind, it's easily the city's most memorable structure. Begun in the late 1940s and completed in 1974, the church is named after Iceland's best-known poet, Hallgrímur Pétursson. You can wander its stark, light-filled interior, then take a lift to the top of a 75m-high (246ft) tower which offers superb views of the city. On the lawn is a statue of Leif Eriksson, triumphantly identified as the 'Son of Iceland, Discoverer of Vinland' (believed to be Newfoundland or Labrador).

Another place with an outwardly tacky appearance is the Volcano Show. Again, don't be put off by the design; this theatre offers invaluable insights into the volcanic spectre under (or over) which Icelanders live. Here you can see dramatic film of some of the country's greatest volcanic eruptions, including one award-winning film of the birth of Surtsey, which belched and spewed its way - Exorcist-like - out of the sea in 1963. Other sights include a pleasant botanic garden, a popular recreational park and a number of museums dedicated to the works of Iceland's leading artists.

Budget accommodation, cheap eats and bargain shopping are found in or just east of the Old Town. For entertainment, there's cinema (films are screened in their original language with Icelandic subtitles), cultural performances (theatre, opera, symphony, and dance) and light shows (sagas, Settlement and Viking extravaganzas). Runtur is a bit of a Reykjavík institution, which involves trawling through the city's hip bars, live music venues and discos to make sure no-one's missing the best action.

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• Destination Iceland

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